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Publications Bernd Sturmfels
Journal Articles
Améndola, Carlos ; Friz, Peter and Bernd Sturmfels:
Varieties of signature tensors
In: Forum of mathematics / Sigma,
7 (2019), e10
Bibtex MIS-Preprint: 33/2018 DOI: 10.1017/fms.2019.3 ARXIV: https://arxiv.org/abs/1804.08325Chua, Lynn ; Kummer, Mario and Bernd Sturmfels:
Schottky algorithms : classical meets tropical
In: Mathematics of computation,
88 (2019) 319, p. 2541-2558
Bibtex MIS-Preprint: 42/2017 DOI: 10.1090/mcom/3406 ARXIV: https://arxiv.org/abs/1707.08520Cifuentes, Diego ; Harris, Corey and Bernd Sturmfels:
The geometry of SDP-exactness in quadratic optimization
In: Mathematical programming,
Vol. not yet known, pp. not yet known
Bibtex MIS-Preprint: 28/2018 DOI: 10.1007/s10107-019-01399-8 ARXIV: https://arxiv.org/abs/1804.01796Kaihnsa, Nidhi ; Kummer, Mario ; Plaumann, Daniel ; Sayyary Namin, Mahsa and Bernd Sturmfels:
Sixty-four curves of degree six
In: Experimental mathematics,
28 (2019) 2, p. 132-150
Bibtex MIS-Preprint: 23/2017 DOI: 10.1080/10586458.2017.1360808 ARXIV: https://arxiv.org/abs/1703.01660Pfeffer, Max ; Seigal, Anna and Bernd Sturmfels:
Learning paths from signature tensors
In: SIAM journal on matrix analysis and applications,
40 (2019) 2, p. 394-416
Bibtex MIS-Preprint: 78/2018 DOI: 10.1137/18M1212331 ARXIV: https://arxiv.org/abs/1809.01588Robeva, Elina ; Sturmfels, Bernd and Caroline Uhler:
Geometry of log-concave density estimation
In: Discrete and computational geometry,
61 (2019) 1, p. 136-160
Bibtex MIS-Preprint: 32/2017 DOI: 10.1007/s00454-018-0024-y ARXIV: https://arxiv.org/abs/1704.01910Améndola, Carlos ; Ranestad, Kristian and Bernd Sturmfels:
Algebraic identifiability of Gaussian mixtures
In: International mathematics research notices,
2018 (2018) 21, p. 6556-6580
Bibtex MIS-Preprint: 76/2016 DOI: 10.1093/imrn/rnx090 ARXIV: https://arxiv.org/abs/1612.01129Boege, Tobias ; D'Ali, Alessio ; Kahle, Thomas and Bernd Sturmfels:
The geometry of Gaussoids
In: Foundations of computational mathematics,
Vol. not yet known, pp. not yet known
Bibtex MIS-Preprint: 70/2017 DOI: 10.1007/s10208-018-9396-x ARXIV: https://arxiv.org/abs/1710.07175Breiding, Paul ; Kališnik Verovšek, Sara ; Sturmfels, Bernd and Madeleine Weinstein:
Learning algebraic varieties from samples
In: Revista matematica complutense,
31 (2018) 3, p. 545-593
Bibtex MIS-Preprint: 23/2018 DOI: 10.1007/s13163-018-0273-6 ARXIV: https://arxiv.org/abs/1802.09436Helmer, Martin and Bernd Sturmfels:
Nearest points on toric varieties
In: Mathematica Scandinavica,
122 (2018) 2, p. 213-238
Bibtex DOI: 10.7146/math.scand.a-101478 ARXIV: http://arxiv.org/abs/1603.06544Kileel, Joe ; Kukelova, Zuzana ; Pajdla, Tomas and Bernd Sturmfels:
Distortion varieties
In: Foundations of computational mathematics,
18 (2018) 4, p. 1043-1071
Bibtex DOI: 10.1007/s10208-017-9361-0 ARXIV: https://arxiv.org/abs/1610.01860Kohn, Kathlén ; Sturmfels, Bernd and Matthew Trager:
Changing views on curves and surfaces
In: Acta mathematica Vietnamica,
43 (2018) 1, p. 1-29
Bibtex MIS-Preprint: 39/2017 DOI: 10.1007/s40306-017-0240-1 ARXIV: https://arxiv.org/abs/1707.01877Michałek, Mateusz and Bernd Sturmfels:
Tensoren und ihre Zerlegungen
In: Jahrbuch der Max-Planck-Gesellschaft,
2018 (2018), Forschungsbericht - Max-Planck-Institut für Mathematik in den Naturwissenschaften
Bibtex LINK: https://www.mpg.de/11715171/mpi_mis_jb_2018?c=12090594Agarwal, Sameer ; Lee, Hon-Leung ; Sturmfels, Bernd and Rekha R. Thomas:
On the existence of epipolar matrices
In: International journal of computer vision,
121 (2017) 3, p. 403-415
Bibtex DOI: 10.1007/s11263-016-0949-7 ARXIV: http://arxiv.org/abs/1510.01401Drton, Mathias ; Kahle, Thomas ; Sturmfels, Bernd and Caroline Uhler:
Algebraic statistics : 16 April - 22 April 2017 ; report no. 20/2017
In: Oberwolfach reports,
14 (2017) 2, p. 1207-1279
Bibtex DOI: 10.4171/OWR/2017/20Lin, Bo ; Sturmfels, Bernd ; Tang, Xiaoxian and Ruriko Yoshida:
Convexity in tree spaces
In: SIAM journal on discrete mathematics,
31 (2017) 3, p. 2015-2038
Bibtex DOI: 10.1137/16M1079841 ARXIV: http://arxiv.org/abs/1510.08797Michałek, Mateusz ; Moon, Hyunsuk ; Sturmfels, Bernd and Emanuele Ventura:
Real rank geometry of ternary forms
In: Annali di matematica pura ed applicata,
196 (2017) 3, p. 1025-1054
Bibtex DOI: 10.1007/s10231-016-0606-3 ARXIV: http://arxiv.org/abs/1601.06574Ponce, Jean ; Sturmfels, Bernd and Matthew Trager:
Congruences and concurrent lines in multi-view geometry
In: Advances in applied mathematics,
88 (2017), p. 62-91
Bibtex DOI: 10.1016/j.aam.2017.01.001 ARXIV: http://de.arxiv.org/abs/1608.05924Seigal, Anna ; Mira, Portia M. ; Sturmfels, Bernd and Miriam Barlow:
Does antibiotic resistance evolve in hospitals?
In: Bulletin of mathematical biology,
79 (2017) 1, p. 191-208
Bibtex DOI: 10.1007/s11538-016-0232-7 ARXIV: http://arxiv.org/abs/1605.03660Seigal, Anna and Bernd Sturmfels:
Real rank two geometry
In: Journal of algebra,
484 (2017), p. 310-333
Bibtex DOI: 10.1016/j.jalgebra.2017.04.014 ARXIV: https://arxiv.org/abs/1609.09245Sturmfels, Bernd:
The Hurwitz form of a projective variety
In: Journal of symbolic computation,
79 (2017) 1, p. 186-196
Bibtex DOI: 10.1016/j.jsc.2016.08.012 ARXIV: http://arxiv.org/abs/1410.6703Sturmfels, Bernd:
Message from the editor-in-chief
In: SIAM journal on applied algebra and geometry,
1 (2017) 1, p. 1-1
Bibtex DOI: 10.1137/17N974240Améndola, Carlos ; Faugère, Jean-Charles and Bernd Sturmfels:
Moment varieties of Gaussian mixtures
In: Journal of algebraic statistics,
7 (2016) 1, p. 14-28
Bibtex DOI: 10.18409/jas.v7i1.42 ARXIV: http://arxiv.org/abs/1510.04654Draisma, Jan ; Horobet, Emil ; Ottaviani, Giorgio ; Sturmfels, Bernd and Rekha R. Thomas:
The Euclidean distance degree of an algebraic variety
In: Foundations of computational mathematics,
16 (2016) 1, p. 99-149
Bibtex DOI: 10.1007/s10208-014-9240-x ARXIV: http://arxiv.org/abs/1309.0049Gross, Elizabeth ; Harrington, Heather A. ; Rosen, Zvi and Bernd Sturmfels:
Algebraic systems biology : a case study for the Wnt pathway
In: Bulletin of mathematical biology,
78 (2016) 1, p. 21-51
Bibtex DOI: 10.1007/s11538-015-0125-1 ARXIV: http://arxiv.org/abs/1502.03188Joswig, Michael ; Kileel, Joe ; Sturmfels, Bernd and André Wagner:
Rigid multiview varieties
In: International journal of algebra and computation,
26 (2016) 4, p. 775-788
Bibtex DOI: 10.1142/S021819671650034X ARXIV: http://arxiv.org/abs/1509.03257Lee, Hwangrae and Bernd Sturmfels:
Duality of multiple root loci
In: Journal of algebra,
446 (2016), p. 499-526
Bibtex DOI: 10.1016/j.jalgebra.2015.08.029 ARXIV: http://arxiv.org/abs/1508.00202Michałek, Mateusz ; Sturmfels, Bernd ; Uhler, Caroline and Piotr Zwiernik:
Exponential varieties
In: Proceedings of the London Mathematical Society,
112 (2016) 1, p. 27-56
Bibtex DOI: 10.1112/plms/pdv066 ARXIV: http://arxiv.org/abs/1412.6185Oeding, Luke ; Robeva, Elina and Bernd Sturmfels:
Decomposing tensors into frames
In: Advances in applied mathematics,
73 (2016), p. 125-153
Bibtex DOI: 10.1016/j.aam.2015.10.004 ARXIV: http://arxiv.org/abs/1504.08049Ren, Qingchun ; Shaw, Kristin and Bernd Sturmfels:
Tropicalization of del Pezzo surfaces
In: Advances in mathematics,
300 (2016), p. 156-189
Bibtex DOI: 10.1016/j.aim.2016.03.017 ARXIV: http://arxiv.org/abs/1402.5651Sturmfels, Bernd:
Tensors and their eigenvectors
In: Notices of the American Mathematical Society,
63 (2016) 6, p. 604-606
Bibtex DOI: 10.1090/noti1389Sturmfels, Bernd ; Tsukerman, Emmanuel and Lauren Williams:
Symmetric matrices, Catalan paths, and correlations
In: Journal of combinatorial theory / A,
144 (2016), p. 496-510
Bibtex DOI: 10.1016/j.jcta.2016.06.014 ARXIV: http://arxiv.org/abs/1511.04125Allman, Elizabeth S. ; Rhodes, John A. ; Sturmfels, Bernd and Piotr Zwiernik:
Tensors of nonnegative rank two
In: Linear algebra and its applications,
473 (2015), p. 37-53
Bibtex DOI: 10.1016/j.laa.2013.10.046 ARXIV: http://arxiv.org/abs/1305.0539Brodsky, Sarah ; Joswig, Michael ; Morrison, Ralph and Bernd Sturmfels:
Moduli of tropical plane curves
In: Research in the mathematical sciences,
2 (2015), 4
Bibtex DOI: 10.1186/s40687-014-0018-1 ARXIV: http://arxiv.org/abs/1409.4395Kateri, Maria ; Mohammadi, Fatemeh and Bernd Sturmfels:
A family of quasisymmetry models
In: Journal of algebraic statistics,
6 (2015) 1, p. 1-16
Bibtex DOI: 10.18409/jas.v6i1.33 ARXIV: http://arxiv.org/abs/1403.0547Kubjas, Kaie ; Robeva, Elina and Bernd Sturmfels:
Fixed points of the EM algorithm and nonnegative rank boundaries
In: The annals of statistics,
43 (2015) 1, p. 422-461
Bibtex DOI: 10.1214/14-AOS1282 ARXIV: http://arxiv.org/abs/1312.5634Mira, Portia M. ; Crona, Kristina ; Greene, Devin ; Meza, Juan C. ; Sturmfels, Bernd and Miriam Barlow:
Rational design of antibiotic treatment plans : a treatment strategy for managing
evolution and reversing resistance
In: PLoS one,
10 (2015) 5, e0122283
Bibtex DOI: 10.1371/journal.pone.0122283 ARXIV: http://de.arxiv.org/abs/1406.1564Mira, Portia M. ; Crona, Kristina ; Greene, Devin ; Meza, Juan C. ; Sturmfels, Bernd and Miriam Barlow:
Correction: Rational design of antibiotic treatment plans : a treatment strategy for
managing evolution and reversing resistance (vol 10, e0122283, 2015)
In: PLoS one,
10 (2015) 9, e0139387
Bibtex DOI: 10.1371/journal.pone.0139387Ottem, John Christian ; Ranestad, Kristian ; Sturmfels, Bernd and Cynthia Vinzant:
Quartic spectrahedra
In: Mathematical programming,
151 (2015) 2, p. 585-612
Bibtex DOI: 10.1007/s10107-014-0844-3 ARXIV: http://arxiv.org/abs/1311.3675Ren, Qingchun ; Richter-Gebert, Jürgen and Bernd Sturmfels:
Cayley-Bacharach formulas
In: The American mathematical monthly,
122 (2015) 9, p. 845-854
Bibtex DOI: 10.4169/amer.math.monthly.122.9.845 ARXIV: http://arxiv.org/abs/1405.6438Sinn, Rainer and Bernd Sturmfels:
Generic spectrahedral shadows
In: SIAM journal on optimization,
25 (2015) 2, p. 1209-1220
Bibtex DOI: 10.1137/140978478 ARXIV: http://arxiv.org/abs/1407.5219Hauenstein, Jonathan ; Rodriguez, Jose Israel and Bernd Sturmfels:
Maximum likelihood for matrices with rank constraints
In: Journal of algebraic statistics,
5 (2014) 1, p. 18-38
Bibtex DOI: 10.18409/jas.v5i1.23 ARXIV: http://arxiv.org/abs/1210.0198Lin, Shaowei ; Uhler, Caroline ; Sturmfels, Bernd and Peter Bühlmann:
Hypersurfaces and their singularities in partial correlation testing
In: Foundations of computational mathematics,
14 (2014) 5, p. 1079-1116
Bibtex DOI: 10.1007/s10208-014-9205-0 ARXIV: http://arxiv.org/abs/1209.0285Ottaviani, Giorgio ; Spaenlehauer, Pierre-Jean and Bernd Sturmfels:
Exact solutions in structured low-rank approximation
In: SIAM journal on matrix analysis and applications,
35 (2014) 4, p. 1521-1542
Bibtex DOI: 10.1137/13094520X ARXIV: http://arxiv.org/abs/1311.2376Ren, Qingchun ; Sam, Steven V. and Bernd Sturmfels:
Tropicalization of classical moduli spaces
In: Mathematics in computer science,
8 (2014) 2, p. 119-145
Bibtex DOI: 10.1007/s11786-014-0185-x ARXIV: http://arxiv.org/abs/1303.1132Aholt, Chris ; Sturmfels, Bernd and Rekha R. Thomas:
A Hilbert scheme in computer vision
In: Canadian journal of mathematics,
65 (2013) 5, p. 961-988
Bibtex DOI: 10.4153/CJM-2012-023-2 ARXIV: http://arxiv.org/abs/1107.2875Cartwright, Dustin and Bernd Sturmfels:
The number of eigenvalues of a tensor
In: Linear algebra and its applications,
438 (2013) 2, p. 942-952
Bibtex DOI: 10.1016/j.laa.2011.05.040 ARXIV: http://arxiv.org/abs/1004.4953Cattani, Eduardo ; Cueto, Maria Angélica ; Dickenstein, Alicia ; Di Rocco, Sandra and Bernd Sturmfels:
Mixed discriminants
In: Mathematische Zeitschrift,
274 (2013) 3-4, p. 761-778
Bibtex DOI: 10.1007/s00209-012-1095-8 ARXIV: http://arxiv.org/abs/1112.1012Engström, Alexander ; Hersh, Patricia and Bernd Sturmfels:
Toric cubes
In: Rendiconti del Circolo Matematico di Palermo,
62 (2013) 1, p. 67-78
Bibtex DOI: 10.1007/s12215-013-0115-9 ARXIV: http://arxiv.org/abs/1202.4333Manjunath, Madhusudan and Bernd Sturmfels:
Monomials, binomials and Riemann-Roch
In: Journal of algebraic combinatorics : an international journal,
37 (2013) 4, p. 737-756
Bibtex DOI: 10.1007/s10801-012-0386-9 ARXIV: http://arxiv.org/abs/1201.4357Morgenshtern, Veniamin I. ; Riegler, Erwin ; Yang, Wei ; Durisi, Giuseppe ; Lin, Shaowei ; Sturmfels, Bernd and Helmut Bölcskei:
Capacity pre-log of noncoherent SIMO channels via Hironaka's theorem
In: IEEE transactions on information theory,
59 (2013) 7, p. 4213-4229
Bibtex DOI: 10.1109/TIT.2013.2251394 ARXIV: http://arxiv.org/abs/1204.2775Ottaviani, Giorgio and Bernd Sturmfels:
Matrices with eigenvectors in a given subspace
In: Proceedings of the American Mathematical Society,
141 (2013) 4, p. 1219-1232
Bibtex DOI: 10.1090/S0002-9939-2012-11404-2 ARXIV: http://arxiv.org/abs/1012.1016Ren, Qingchun ; Sam, Steven V. ; Schrader, Gus and Bernd Sturmfels:
The universal Kummer threefold
In: Experimental mathematics,
22 (2013) 3, p. 327-362
Bibtex DOI: 10.1080/10586458.2013.816206 ARXIV: http://arxiv.org/abs/1208.1229Sanyal, Raman ; Sturmfels, Bernd and Cynthia Vinzant:
The entropic discriminant
In: Advances in mathematics,
244 (2013), p. 678-707
Bibtex DOI: 10.1016/j.aim.2013.05.019 ARXIV: http://arxiv.org/abs/1108.2925Sturmfels, Bernd and Ngoc Mai Tran:
Combinatorial types of tropical eigenvectors
In: The bulletin of the London Mathematical Society,
45 (2013) 1, p. 27-36
Bibtex DOI: 10.1112/blms/bds058 ARXIV: http://arxiv.org/abs/1105.5504Sturmfels, Bernd and Piotr Zwiernik:
Binary cumulant varieties
In: Annals of combinatorics,
17 (2013) 1, p. 229-250
Bibtex DOI: 10.1007/s00026-012-0174-1 ARXIV: http://arxiv.org/abs/1103.0153Blekherman, Grigoriy ; Hauenstein, Jonathan ; Ottem, John Christian ; Ranestad, Kristian and Bernd Sturmfels:
Algebraic boundaries of Hilbert's SOS cones
In: Compositio mathematica,
148 (2012) 6, p. 1717-1735
Bibtex DOI: 10.1112/S0010437X12000437 ARXIV: http://arxiv.org/abs/1107.1846De Loera, Jesús A. ; Sturmfels, Bernd and Cynthia Vinzant:
The central curve in linear programming
In: Foundations of computational mathematics,
12 (2012) 4, p. 509-540
Bibtex DOI: 10.1007/s10208-012-9127-7 ARXIV: http://arxiv.org/abs/1012.3978Filiz, Ismail Onur ; Guo, Xin ; Morton, Jason and Bernd Sturmfels:
Graphical models for correlated defaults
In: Mathematical finance : an international journal of mathematics, statistics and financial
economics,
22 (2012) 4, p. 621-644
Bibtex DOI: 10.1111/j.1467-9965.2011.00499.x ARXIV: https://arxiv.org/abs/0809.1393Ranestad, Kristian and Bernd Sturmfels:
On the convex hull of a space curve
In: Advances in geometry,
12 (2012) 1, p. 157-178
Bibtex DOI: 10.1515/advgeom.2011.021 ARXIV: http://arxiv.org/abs/0912.2986Sturmfels, Bernd:
Geometry of higher-order Markov chains
In: Journal of algebraic statistics,
3 (2012) 1, p. 1-10
Bibtex DOI: 10.18409/jas.v3i1.13 ARXIV: http://arxiv.org/abs/1207.1899Sturmfels, Bernd and Volkmar Welker:
Commutative algebra of statistical ranking
In: Journal of algebra,
361 (2012), p. 264-286
Bibtex DOI: 10.1016/j.jalgebra.2012.03.028 ARXIV: http://arxiv.org/abs/1101.1597Brodsky, Sarah B. and Bernd Sturmfels:
Tropical quadrics through three points
In: Linear algebra and its applications,
435 (2011) 7, p. 1778-1785
Bibtex DOI: 10.1016/j.laa.2010.05.004 ARXIV: http://arxiv.org/abs/1002.0603Cartwright, Dustin ; Häbich, Mathias ; Sturmfels, Bernd and Annette Werner:
Mustafin varieties
In: Selecta mathematica,
17 (2011) 4, p. 757-793
Bibtex DOI: 10.1007/s00029-011-0075-x ARXIV: http://arxiv.org/abs/1002.1418Plaumann, Daniel ; Sturmfels, Bernd and Cynthia Vinzant:
Quartic curves and their bitangents
In: Journal of symbolic computation,
46 (2011) 6, p. 712-733
Bibtex DOI: 10.1016/j.jsc.2011.01.007 ARXIV: http://arxiv.org/abs/1008.4104Sanyal, Raman ; Sottile, Frank and Bernd Sturmfels:
Orbitopes
In: Mathematika : a journal of pure and applied mathematics,
57 (2011) 2, p. 275-314
Bibtex DOI: 10.1112/S002557931100132X ARXIV: http://arxiv.org/abs/0911.5436Cartwright, Dustin and Bernd Sturmfels:
The Hilbert scheme of the diagonal in a product of projective spaces
In: International mathematics research notices,
2010 (2010) 9, p. 1741-1771
Bibtex DOI: 10.1093/imrn/rnp201 ARXIV: http://arxiv.org/abs/0901.0212Evans, Steven N. ; Sturmfels, Bernd and Caroline Uhler:
Commuting birth-and-death processes
In: The annals of applied probability,
20 (2010) 1, p. 238-266
Bibtex DOI: 10.1214/09-AAP615 ARXIV: http://arxiv.org/abs/0812.2724Nie, Jiawang ; Ranestad, Kristian and Bernd Sturmfels:
The algebraic degree of semidefinite programming
In: Mathematical programming,
122 (2010) 2, p. 379-405
Bibtex DOI: 10.1007/s10107-008-0253-6 ARXIV: https://arxiv.org/abs/math/0611562Rostalski, Philipp and Bernd Sturmfels:
Dualities in convex algebraic geometry
In: Rendiconti di matematica e delle sue applicazioni,
30 (2010) 3-4, p. 285-327
Bibtex ARXIV: http://arxiv.org/abs/1006.4894 LINK: http://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2010%283-4%29/285-327.pdfShiu, Anne and Bernd Sturmfels:
Siphons in chemical reaction networks
In: Bulletin of mathematical biology,
72 (2010) 6, p. 1448-1463
Bibtex DOI: 10.1007/s11538-010-9502-y ARXIV: http://arxiv.org/abs/0904.4529Sturmfels, Bernd and Caroline Uhler:
Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry
In: Annals of the institute of statistical mathematics,
62 (2010) 4, p. 603-638
Bibtex DOI: 10.1007/s10463-010-0295-4 ARXIV: http://arxiv.org/abs/0906.3529Sturmfels, Bernd and Mauricio Velasco:
Blow-ups of \(\mathbb{P}^{n-3}\) at \(n\) points and spinor varieties
In: Journal of commutative algebra,
2 (2010) 2, p. 223-244
Bibtex DOI: 10.1216/JCA-2010-2-2-223 ARXIV: http://arxiv.org/abs/0906.5096Sturmfels, Bernd and Zhiqiang Xu:
Sagbi bases of Cox-Nagata rings
In: Journal of the European Mathematical Society,
12 (2010) 2, p. 429-459
Bibtex DOI: 10.4171/JEMS/204 ARXIV: https://arxiv.org/abs/0803.0892Cartwright, Dustin A. ; Brady, Siobhan M. ; Orlando, David A. ; Sturmfels, Bernd and Philip N. Benfey:
Reconstructing spatiotemporal gene expression data from partial observations
In: Bioinformatics,
25 (2009) 19, p. 2581-2587
Bibtex DOI: 10.1093/bioinformatics/btp437 ARXIV: http://arxiv.org/abs/0903.4027Craciun, Gheorghe ; Dickenstein, Alicia ; Shiu, Anne and Bernd Sturmfels:
Toric dynamical systems
In: Journal of symbolic computation,
44 (2009) 11, p. 1551-1565
Bibtex DOI: 10.1016/j.jsc.2008.08.006 ARXIV: http://arxiv.org/abs/0708.3431Dueck, Pierre ; Hosten, Serkan and Bernd Sturmfels:
Normal toric ideals of low codimension
In: Journal of pure and applied algebra,
213 (2009) 8, p. 1636-1641
Bibtex DOI: 10.1016/j.jpaa.2008.11.045 ARXIV: http://arxiv.org/abs/0801.3826Gritzmann, Peter ; Sturmfels, Bernd and Günter M. Ziegler:
Guest editors' foreword : [special issue dedicated to the memory of Victor Klee]
In: Discrete and computational geometry,
42 (2009) 2, p. 131-131
Bibtex DOI: 10.1007/s00454-009-9191-1Herrmann, Sven ; Jensen, Anders ; Joswig, Michael and Bernd Sturmfels:
How to draw tropical planes
In: The electronic journal of combinatorics,
16 (2009) 2, R6
Bibtex ARXIV: http://arxiv.org/abs/0808.2383 LINK: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v16i2r6Laubenbacher, Reinhard and Bernd Sturmfels:
Computer algebra in systems biology
In: The American mathematical monthly,
116 (2009) 10, p. 882-891
Bibtex DOI: 10.4169/000298909X477005 ARXIV: http://arxiv.org/abs/0712.4248Laubenbacher, Reinhard and Bernd Sturmfels:
Computeralgebra in der Systembiologie
In: Informatik-Spektrum,
32 (2009) 1, p. 27-32
Bibtex DOI: 10.1007/s00287-008-0307-4Lin, Shaowei and Bernd Sturmfels:
Polynomial relations among principal minors of a 4 x 4-matrix
In: Journal of algebra,
322 (2009) 11, p. 4121-4131
Bibtex DOI: 10.1016/j.jalgebra.2009.06.026 ARXIV: http://arxiv.org/abs/0812.0601Lin, Shaowei ; Sturmfels, Bernd and Zhiqiang Xu:
Marginal likelihood integrals for mixtures of independence models
In: Journal of machine learning research,
10 (2009), p. 1611-1631
Bibtex ARXIV: http://arxiv.org/abs/0805.3602 LINK: http://www.jmlr.org/papers/volume10/lin09a/lin09a.pdfMorton, Jason ; Pachter, Lior ; Shiu, Anne ; Sturmfels, Bernd and Oliver Wienand:
Convex rank tests and semigraphoids
In: SIAM journal on discrete mathematics,
23 (2009) 3, p. 1117-1134
Bibtex DOI: 10.1137/080715822 ARXIV: http://arxiv.org/abs/math/0702564Nie, Jiawang and Bernd Sturmfels:
Matrix cubes parameterized by eigenvalues
In: SIAM journal on matrix analysis and applications,
31 (2009) 2, p. 755-766
Bibtex DOI: 10.1137/080722606 ARXIV: http://arxiv.org/abs/0804.4462Speyer, David and Bernd Sturmfels:
Tropical mathematics
In: Mathematics magazine,
82 (2009) 3, p. 163-173
Bibtex ARXIV: http://arxiv.org/abs/math/0408099 LINK: http://www.jstor.org/stable/27765897Bogart, Tristram ; Jensen, Anders ; Speyer, David ; Sturmfels, Bernd and Rekha R. Thomas:
Computing tropical varieties
In: Topologica,
1 (2008) 1, P 007
Bibtex DOI: 10.3731/topologica.1.007 ARXIV: http://arxiv.org/abs/math/0507563Dequéant, Mary-Lee ; Ahnert, Sebastian ; Edelsbrunner, Herbert ; Fink, Thomas M. A. ; Glynn, Earl F. ; Hattem, Gaye ; Kudlicki, Andrzej ; Mileyko, Yuriy ; Morton, Jason ; Mushegian, Arcady R. ; Pachter, Lior ; Rowicka, Maga ; Shiu, Anne ; Sturmfels, Bernd and Olivier Pourquié:
Comparison of pattern detection methods in microarray time series of the segmentation
clock
In: PLoS one,
3 (2008) 8, e2856
Bibtex DOI: 10.1371/journal.pone.0002856Gritzmann, Peter and Bernd Sturmfels:
Victor L. Klee 1925-2007
In: Notices of the American Mathematical Society,
55 (2008) 4, p. 467-473
Bibtex LINK: http://www.ams.org/notices/200804/tx080400467p.pdfHemmecke, Raymond ; Morton, Jason ; Shiu, Anne ; Sturmfels, Bernd and Oliver Wienand:
Three counter-examples on semi-graphoids
In: Combinatorics, probability and computing,
17 (2008) 02, p. 239-257
Bibtex DOI: 10.1017/S0963548307008838 ARXIV: https://arxiv.org/abs/math/0610451Huggins, Peter ; Sturmfels, Bernd ; Yu, Josephine and Debbie S. Yuster:
The hyperdeterminant and triangulations of the 4-cube
In: Mathematics of computation,
77 (2008) 263, p. 1653-1679
Bibtex ARXIV: https://arxiv.org/abs/math/0602149 LINK: http://www.jstor.org/stable/40234576Sturmfels, Bernd and Seth Sullivant:
Toric geometry of cuts and splits
In: The Michigan mathematical journal,
57 (2008), p. 689-709
Bibtex DOI: 10.1307/mmj/1220879432 ARXIV: https://arxiv.org/abs/math/0606683Sturmfels, Bernd and Jenia Tevelev:
Elimination theory for tropical varieties
In: Mathematical research letters,
15 (2008) 3, p. 543-562
Bibtex DOI: 10.4310/MRL.2008.v15.n3.a14 ARXIV: http://arxiv.org/abs/0704.3471Beerenwinkel, Niko ; Eriksson, Nicholas and Bernd Sturmfels:
Conjunctive Bayesian networks
In: Bernoulli,
13 (2007) 4, p. 893-909
Bibtex DOI: 10.3150/07-BEJ6133 ARXIV: http://arxiv.org/abs/math/0608417Beerenwinkel, Niko ; Pachter, Lior and Bernd Sturmfels:
Epistasis and shapes of fitness landscapes
In: Statistica Sinica,
17 (2007) 4, p. 1317-1342
Bibtex ARXIV: http://arxiv.org/abs/q-bio/0603034 LINK: http://www.jstor.org/stable/24307677Beerenwinkel, Niko ; Pachter, Lior ; Sturmfels, Bernd ; Elena, Santiago F. and Richard E. Lenski:
Analysis of epistatic interactions and fitness landscapes using a new geometric approach
In: BMC evolutionary biology,
7 (2007), 60
Bibtex DOI: 10.1186/1471-2148-7-60Bogart, Tristram ; Jensen, Anders ; Speyer, David ; Sturmfels, Bernd and Rekha R. Thomas:
Computing tropical varieties
In: Journal of symbolic computation,
42 (2007) 1-2, p. 54-73
Bibtex DOI: 10.1016/j.jsc.2006.02.004 ARXIV: http://arxiv.org/abs/math/0507563Dickenstein, Alicia ; Feichtner, Eva Maria and Bernd Sturmfels:
Tropical discriminants
In: Journal of the American Mathematical Society,
20 (2007) 4, p. 1111-1133
Bibtex DOI: 10.1090/S0894-0347-07-00562-0 ARXIV: http://arxiv.org/abs/math/0510126Drton, Mathias ; Sturmfels, Bernd and Seth Sullivant:
Algebraic factor analysis : tetrads, pentads and beyond
In: Probability theory and related fields,
138 (2007) 3-4, p. 463-493
Bibtex DOI: 10.1007/s00440-006-0033-2 ARXIV: http://arxiv.org/abs/math/0509390Holtz, Olga and Bernd Sturmfels:
Hyperdeterminantal relations among symmetric principal minors
In: Journal of algebra,
316 (2007) 2, p. 634-648
Bibtex DOI: 10.1016/j.jalgebra.2007.01.039 ARXIV: http://arxiv.org/abs/math/0604374Hosten, Serkan and Bernd Sturmfels:
Computing the integer programming gap
In: Combinatorica,
27 (2007) 3, p. 367-382
Bibtex DOI: 10.1007/s00493-007-2057-3 ARXIV: http://arxiv.org/abs/math/0301266Huggins, Peter ; Pachter, Lior and Bernd Sturmfels:
Toward the human genotope
In: Bulletin of mathematical biology,
69 (2007) 8, p. 2723-2735
Bibtex DOI: 10.1007/s11538-007-9244-7 ARXIV: http://arxiv.org/abs/q-bio/0611032Joswig, Michael ; Sturmfels, Bernd and Josephine Yu:
Affine buildings and tropical convexity
In: Albanian journal of mathematics,
1 (2007) 4, p. 187-211
Bibtex ARXIV: http://arxiv.org/abs/0706.1918Morton, Jason ; Pachter, Lior ; Shiu, Anne and Bernd Sturmfels:
The cyclohedron test for finding periodic genes in time course expression studies
In: Statistical applications in genetics and molecular biology,
6 (2007) 1, 21
Bibtex DOI: 10.2202/1544-6115.1286 ARXIV: http://arxiv.org/abs/q-bio/0702049Pachter, Lior and Bernd Sturmfels:
The mathematics of phylogenomics
In: SIAM review,
49 (2007) 1, p. 3-31
Bibtex DOI: 10.1137/050632634 ARXIV: http://arxiv.org/abs/math/0409132Sturmfels, Bernd ; Tevelev, Jenia and Josephine Yu:
The Newton polytope of the implicit equation
In: Moscow mathematical journal,
7 (2007) 2, p. 327-346
Bibtex ARXIV: http://arxiv.org/abs/math/0607368 LINK: http://www.ams.org/distribution/mmj/vol7-2-2007/abst7-2-2007.html#sturmfels-tevelev-yuBeerenwinkel, Niko ; Eriksson, Nicholas and Bernd Sturmfels:
Evolution on distributive lattices
In: Journal of theoretical biology,
242 (2006) 2, p. 409-420
Bibtex DOI: 10.1016/j.jtbi.2006.03.013 ARXIV: http://arxiv.org/abs/q-bio/0511039Catanese, Fabrizio ; Hosten, Serkan ; Khetan, Amit and Bernd Sturmfels:
The maximum likelihood degree
In: American journal of mathematics,
128 (2006) 3, p. 671-697
Bibtex DOI: 10.1353/ajm.2006.0019 ARXIV: http://arxiv.org/abs/math/0406533Colón-Reyes, Omar ; Jarrah, Abdul Salam ; Laubenbacher, Reinhard and Bernd Sturmfels:
Monomial dynamical systems over finite fields
In: Complex systems,
16 (2006) 4, p. 333-342
Bibtex ARXIV: http://arxiv.org/abs/math/0605439 LINK: http://www.complex-systems.com/abstracts/v16_i04_a04.htmlDewey, Colin N. ; Huggins, Peter M. ; Woods, Kevin ; Sturmfels, Bernd and Lior Pachter:
Parametric alignment of Drosophila genomes
In: PLoS computational biology,
2 (2006) 6, p. 606-614
Bibtex DOI: 10.1371/journal.pcbi.0020073 ARXIV: http://arxiv.org/abs/q-bio/0512008Geiger, Dan ; Meek, Christopher and Bernd Sturmfels:
On the toric algebra of graphical models
In: The annals of statistics,
34 (2006) 3, p. 1463-1492
Bibtex DOI: 10.1214/009053606000000263 ARXIV: https://arxiv.org/abs/math/0608054Hallgrimsdóttir, Ingileif B. and Bernd Sturmfels:
Resultants in genetic linkage analysis
In: Journal of symbolic computation,
41 (2006) 2, p. 125-137
Bibtex DOI: 10.1016/j.jsc.2005.04.012 ARXIV: http://arxiv.org/abs/q-bio/0405001Nie, Jiawang ; Demmel, James and Bernd Sturmfels:
Minimizing polynomials via sum of squares over the gradient ideal
In: Mathematical programming,
106 (2006) 3, p. 587-606
Bibtex DOI: 10.1007/s10107-005-0672-6 ARXIV: http://arxiv.org/abs/math/0411342Sturmfels, Bernd and Seth Sullivant:
Combinatorial secant varieties
In: Pure and applied mathematics quarterly,
2 (2006) 3, p. 867-891
Bibtex DOI: 10.4310/PAMQ.2006.v2.n3.a12 ARXIV: http://arxiv.org/abs/math/0506223Altmann, Klaus and Bernd Sturmfels:
The graph of monomial ideals
In: Journal of pure and applied algebra,
201 (2005) 1-3, p. 250-263
Bibtex DOI: 10.1016/j.jpaa.2004.12.030 ARXIV: http://arxiv.org/abs/math/0209152Feichtner, Eva Maria and Bernd Sturmfels:
Matroid polytopes, nested sets and Bergman fans
In: Portugaliae mathematica,
62 (2005) 4, p. 437-468
Bibtex ARXIV: http://arxiv.org/abs/math/0411260 LINK: http://www.emis.ams.org/journals/PM/62f4/3.htmlGarcia, Luis David ; Stillman, Michael E. and Bernd Sturmfels:
Algebraic geometry of Bayesian networks
In: Journal of symbolic computation,
39 (2005) 3-4, p. 331-355
Bibtex DOI: 10.1016/j.jsc.2004.11.007 ARXIV: http://arxiv.org/abs/math/0301255Hosten, Serkan ; Khetan, Amit and Bernd Sturmfels:
Solving the likelihood equations
In: Foundations of computational mathematics,
5 (2005) 4, p. 389-407
Bibtex DOI: 10.1007/s10208-004-0156-8 ARXIV: http://arxiv.org/abs/math/0408270Sturmfels, Bernd:
What is a Gröbner basis?
In: Notices of the American Mathematical Society,
52 (2005) 10, p. 1199-1200
Bibtex LINK: http://www.ams.org/publications/notices/whatis/noticesarchiveSturmfels, Bernd:
Can biology lead to new theorems?
In: Annual report of the Clay Mathematics Institute,
2005 (2005), p. 13-26
Bibtex LINK: http://groups.claymath.org/library/annual_report/ar2005/05report_featurearticle.pdfSturmfels, Bernd and Seth Sullivant:
Toric ideals of phylogenetic invariants
In: Journal of computational biology,
12 (2005) 2, p. 204-228
Bibtex DOI: 10.1089/cmb.2005.12.204 ARXIV: http://arxiv.org/abs/q-bio/0402015De Loera, Jesús A. ; Haws, David ; Hemmecke, Raymond ; Huggins, Peter ; Sturmfels, Bernd and Ruriko Yoshida:
Short rational functions for toric algebra and applications
In: Journal of symbolic computation,
38 (2004) 2, p. 959-973
Bibtex DOI: 10.1016/j.jsc.2004.02.001 ARXIV: https://arxiv.org/abs/math/0307350Develin, Mike and Bernd Sturmfels:
Tropical convexity
In: Documenta mathematica,
9 (2004), p. 1-27
Bibtex ARXIV: http://arxiv.org/abs/math/0308254 LINK: https://www.math.uni-bielefeld.de/documenta/vol-09/01.htmlDevelin, Mike and Bernd Sturmfels:
Erratum for 'Tropical convexity' [Doc. Math. 9 (2004), 1-27]
In: Documenta mathematica,
9 (2004), p. 205-206
Bibtex LINK: http://www.emis.ams.org/journals/DMJDMV/vol-09/12.htmlHaiman, Mark and Bernd Sturmfels:
Multigraded Hilbert schemes
In: Journal of algebraic geometry,
13 (2004) 4, p. 725-769
Bibtex DOI: 10.1090/S1056-3911-04-00373-X ARXIV: http://arxiv.org/abs/math/0201271Hosten, Serkan ; Maclagan, Diane and Bernd Sturmfels:
Supernormal vector configurations
In: Journal of algebraic combinatorics : an international journal,
19 (2004) 3, p. 297-313
Bibtex DOI: 10.1023/B:JACO.0000030705.93448.ce ARXIV: https://arxiv.org/abs/math/0105036Pachter, Lior and Bernd Sturmfels:
Parametric inference for biological sequence analysis
In: Proceedings of the National Academy of Sciences of the United States of America,
101 (2004) 46, p. 16138-16143
Bibtex DOI: 10.1073/pnas.0406011101 ARXIV: http://arxiv.org/abs/q-bio/0401033Pachter, Lior and Bernd Sturmfels:
Tropical geometry of statistical models
In: Proceedings of the National Academy of Sciences of the United States of America,
101 (2004) 46, p. 16132-16137
Bibtex DOI: 10.1073/pnas.0406010101 ARXIV: https://arxiv.org/abs/q-bio/0311009Speyer, David and Bernd Sturmfels:
The tropical Grassmannian
In: Advances in geometry,
4 (2004) 3, p. 389-411
Bibtex DOI: 10.1515/advg.2004.023 ARXIV: http://arxiv.org/abs/math/0304218Sturmfels, Bernd and Josephine Yu:
Classification of six-point metrics
In: The electronic journal of combinatorics,
11 (2004) 1, R44
Bibtex ARXIV: http://arxiv.org/abs/math/0403147 LINK: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v11i1r44De Loera, Jesús A. and Bernd Sturmfels:
Algebraic unimodular counting
In: Mathematical programming,
96 (2003) 2, p. 183-203
Bibtex DOI: 10.1007/s10107-003-0383-9 ARXIV: http://arxiv.org/abs/math/0104286Santos, Francisco and Bernd Sturmfels:
Higher Lawrence configurations
In: Journal of combinatorial theory / A,
103 (2003) 1, p. 151-164
Bibtex DOI: 10.1016/S0097-3165(03)00092-X ARXIV: https://arxiv.org/abs/math/0209326Santos, Francisco and Bernd Sturmfels:
Alexander duality in subdivisions of Lawrence polytopes
In: Advances in geometry,
3 (2003) 2, p. 177-189
Bibtex DOI: 10.1515/advg.2003.012 ARXIV: https://arxiv.org/abs/math/0202104Cattani, Eduardo ; Dickenstein, Alicia and Bernd Sturmfels:
Binomial residues
In: Annales de l'Institut Fourier,
52 (2002) 3, p. 687-708
Bibtex DOI: 10.5802/aif.1898 ARXIV: http://arxiv.org/abs/math/0003178De Loera, Jesús A. ; Sottile, Frank and Bernd Sturmfels:
Guest editors' foreword : [papers from the special session on algebraic and geometric
combinatorics at the AMS Western Section Meeting, San Francisco, CA, USA, October
21-22 and the Bay Area Discrete Math Day, University of California, Davis, CA, USA,
October 20, 2000]
In: Discrete and computational geometry,
27 (2002) 1, p. 1-2
Bibtex DOI: 10.1007/s00454-001-0048-5Dickenstein, Alicia and Bernd Sturmfels:
Elimination theory in codimension 2
In: Journal of symbolic computation,
34 (2002) 2, p. 119-135
Bibtex DOI: 10.1006/jsco.2002.0545 ARXIV: https://arxiv.org/abs/math/0102204Hausel, Tamás and Bernd Sturmfels:
Toric hyperkähler varieties
In: Documenta mathematica,
7 (2002), p. 495-534
Bibtex ARXIV: http://arxiv.org/abs/math/0203096 LINK: https://www.math.uni-bielefeld.de/documenta/vol-07/16.htmlNovik, Isabella ; Postnikov, Alexander and Bernd Sturmfels:
Syzygies of oriented matroids
In: Duke mathematical journal,
111 (2002) 2, p. 287-317
Bibtex DOI: 10.1215/S0012-7094-02-11124-7 ARXIV: https://arxiv.org/abs/math/0009241Bayer, Dave ; Popescu, Sorin and Bernd Sturmfels:
Syzygies of unimodular Lawrence ideals
In: Journal für die reine und angewandte Mathematik,
2001 (2001) 534, p. 169-186
Bibtex DOI: 10.1515/crll.2001.040 ARXIV: https://arxiv.org/abs/math/9912247Cattani, Eduardo ; Dickenstein, Alicia and Bernd Sturmfels:
Rational hypergeometric functions
In: Compositio mathematica,
128 (2001) 2, p. 217-240
Bibtex DOI: 10.1023/A:1017541231618 ARXIV: http://arxiv.org/abs/math/9911030Sottile, Frank and Bernd Sturmfels:
A sagbi basis for the quantum Grassmannian
In: Journal of pure and applied algebra,
158 (2001) 2-3, p. 347-366
Bibtex DOI: 10.1016/S0022-4049(00)00053-0 ARXIV: https://arxiv.org/abs/math/9908016Miller, Ezra ; Sturmfels, Bernd and Kohji Yanagawa:
Generic and cogeneric monomial ideals
In: Journal of symbolic computation,
29 (2000) 4-5, p. 691-708
Bibtex DOI: 10.1006/jsco.1999.0290 ARXIV: http://arxiv.org/abs/math/9812126Sturmfels, Bernd:
Four counterexamples in combinatorial algebraic geometry
In: Journal of algebra,
230 (2000) 1, p. 282-294
Bibtex DOI: 10.1006/jabr.1999.7950Sturmfels, Bernd:
Solving algebraic equations in terms of A-hypergeometric series
In: Discrete mathematics,
210 (2000) 1-3, p. 171-181
Bibtex DOI: 10.1016/S0012-365X(99)00126-0Onn, Shmuel and Bernd Sturmfels:
Cutting corners
In: Advances in applied mathematics,
23 (1999) 1, p. 29-48
Bibtex DOI: 10.1006/aama.1999.0645Saito, Mutsumi ; Sturmfels, Bernd and Nobuki Takayama:
Hypergeometric polynomials and integer programming
In: Compositio mathematica,
115 (1999) 2, p. 231-240
Bibtex DOI: 10.1023/A:1000609524994Sturmfels, Bernd ; Cattani, Eduardo and Alicia Dickenstein:
The search for rational A-hypergeometric functions
In: ACM SIGSAM bulletin,
33 (1999) 3, p. 15-15
Bibtex DOI: 10.1145/347127.347197Bayer, Dave ; Peeva, Irena and Bernd Sturmfels:
Monomial resolutions
In: Mathematical research letters,
5 (1998) 1-2, p. 31-46
Bibtex DOI: 10.4310/MRL.1998.v5.n1.a3 ARXIV: https://arxiv.org/abs/alg-geom/9610012Bayer, Dave and Bernd Sturmfels:
Cellular resolutions of monomial modules
In: Journal für die reine und angewandte Mathematik,
502 (1998), p. 123-140
Bibtex DOI: 10.1515/crll.1998.083 ARXIV: http://arxiv.org/abs/alg-geom/9711023Cattani, Eduardo ; Dickenstein, Alicia and Bernd Sturmfels:
Residues and resultants
In: Journal of mathematical sciences,
5 (1998) 1, p. 119-148
Bibtex ARXIV: https://arxiv.org/abs/alg-geom/9702001 LINK: http://www.ms.u-tokyo.ac.jp/journal/abstract/jms050106.htmlDiaconis, Persi and Bernd Sturmfels:
Algebraic algorithms for sampling from conditional distributions
In: The annals of statistics,
26 (1998) 1, p. 363-397
Bibtex LINK: http://www.jstor.org/stable/119991Eisenbud, David ; Peeva, Irena and Bernd Sturmfels:
Non-commutative Gröbner bases for commutative algebras
In: Proceedings of the American Mathematical Society,
126 (1998) 3, p. 687-691
Bibtex DOI: 10.1090/S0002-9939-98-04229-4Huber, Birkett ; Sottile, Frank and Bernd Sturmfels:
Numerical Schubert calculus
In: Journal of symbolic computation,
26 (1998) 6, p. 767-788
Bibtex DOI: 10.1006/jsco.1998.0239 ARXIV: https://arxiv.org/abs/alg-geom/9706004Peeva, Irena ; Reiner, Victor and Bernd Sturmfels:
How to shell a monoid
In: Mathematische Annalen,
310 (1998) 2, p. 379-393
Bibtex DOI: 10.1007/s002080050152Peeva, Irena and Bernd Sturmfels:
Syzygies of codimension 2 lattice ideals
In: Mathematische Zeitschrift,
229 (1998) 1, p. 163-194
Bibtex DOI: 10.1007/PL00004645Peeva, Irena and Bernd Sturmfels:
Generic lattice ideals
In: Journal of the American Mathematical Society,
11 (1998) 2, p. 363-373
Bibtex LINK: http://www.jstor.org/stable/2646153Roos, Jan-Erik and Bernd Sturmfels:
A toric ring with irrational Poincare-Betti series
In: Comptes rendus de l'Académie des Sciences / 1,
326 (1998) 2, p. 141-146
Bibtex DOI: 10.1016/S0764-4442(97)89459-1Saito, Mutsumi ; Sturmfels, Bernd and Nobuki Takayama:
Gröbner deformations of regular holonomic systems
In: Proceedings of the Japan Academy : series A, mathematical sciences,
74 (1998) 7, p. 111-113
Bibtex DOI: 10.3792/pjaa.74.111Sturmfels, Bernd:
Polynomial equations and convex polytopes
In: The American mathematical monthly,
105 (1998) 10, p. 907-922
Bibtex DOI: 10.2307/2589283Fulton, William and Bernd Sturmfels:
Intersection theory on toric varieties
In: Topology,
36 (1997) 2, p. 335-353
Bibtex DOI: 10.1016/0040-9383(96)00016-X ARXIV: http://de.arxiv.org/abs/alg-geom/9403002Guckenheimer, John ; Myers, Mark and Bernd Sturmfels:
Computing Hopf bifurcations 1.
In: SIAM journal on numerical analysis,
34 (1997) 1, p. 1-21
Bibtex DOI: 10.1137/S0036142993253461Huber, Birkett and Bernd Sturmfels:
Bernstein's theorem in affine space
In: Discrete and computational geometry,
17 (1997) 2, p. 137-141
Bibtex DOI: 10.1007/BF02770870Saito, Mutsumi ; Sturmfels, Bernd and Nobuki Takayama:
Hypergeometric polynomials and integer programming [Japanese]
In: Surikaisekikenkyusho Kokyuroku = RIMS Kokyuroku,
986 (1997), p. 31-33
Bibtex LINK: http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/0986-5.pdfSturmfels, Bernd and Markus Wiegelmann:
Structural Gröbner basis detection
In: Applicable algebra in engineering, communication and computing,
8 (1997) 4, p. 257-263
Bibtex DOI: 10.1007/s002000050063Thomas, Rekha R. and Bernd Sturmfels:
Variation of cost functions in integer programming
In: Mathematical programming,
77 (1997) 2, p. 357-387
Bibtex DOI: 10.1007/BF02614622De Loera, Jesús A. ; Hosten, Serkan ; Santos, Francisco and Bernd Sturmfels:
The polytope of all triangulations of a point configuration
In: Documenta mathematica,
1 (1996), p. 103-119
Bibtex LINK: http://www.emis.ams.org/journals/DMJDMV/vol-01/04.htmlEisenbud, David and Bernd Sturmfels:
Binomial ideals
In: Duke mathematical journal,
84 (1996) 1, p. 1-45
Bibtex DOI: 10.1215/S0012-7094-96-08401-X ARXIV: https://arxiv.org/abs/alg-geom/9401001Laubenbacher, Reinhard and Bernd Sturmfels:
A normal form algorithm for modules over k[x,y]/(xy)
In: Journal of algebra,
184 (1996) 3, p. 1001-1024
Bibtex DOI: 10.1006/jabr.1996.0295De Loera, Jesús A. ; Sturmfels, Bernd and Rekha R. Thomas:
Gröbner bases and triangulations of the second hypersimplex
In: Combinatorica,
15 (1995) 3, p. 409-424
Bibtex DOI: 10.1007/BF01299745Fulton, William ; MacPherson, Robert D. ; Sottile, Frank and Bernd Sturmfels:
Intersection theory on spherical varieties
In: Journal of algebraic geometry,
4 (1995) 1, p. 181-193
Bibtex Huber, Birkett and Bernd Sturmfels:
A polyhedral method for solving sparse polynomial systems
In: Mathematics of computation,
64 (1995) 212, p. 1541-1555
Bibtex DOI: 10.2307/2153370Kalkbrener, Michael and Bernd Sturmfels:
Initial complexes of prime ideals
In: Advances in mathematics,
116 (1995) 2, p. 365-376
Bibtex DOI: 10.1006/aima.1995.1071Sturmfels, Bernd:
On vector partition functions
In: Journal of combinatorial theory / A,
72 (1995) 2, p. 302-309
Bibtex DOI: 10.1016/0097-3165(95)90067-5Sturmfels, Bernd ; Trung, Ngo Viet and Wolfgang Vogel:
Bounds on degrees of projective schemes
In: Mathematische Annalen,
302 (1995) 1, p. 417-432
Bibtex DOI: 10.1007/BF01444501Sturmfels, Bernd ; Weismantel, Robert and Günter M. Ziegler:
Gröbner bases of lattices, corner polyhedra, and integer programming
In: Beiträge zur Algebra und Geometrie,
36 (1995) 2, p. 281-298
Bibtex LINK: http://www.emis.de/journals/BAG/vol.36/no.2/Billera, Louis J. ; Kapranov, Mikhail M. and Bernd Sturmfels:
Cellular strings on polytopes
In: Proceedings of the American Mathematical Society,
122 (1994) 2, p. 549-555
Bibtex DOI: 10.2307/2161048Billera, Louis J. and Bernd Sturmfels:
Iterated fiber polytopes
In: Mathematika : a journal of pure and applied mathematics,
41 (1994) 2, p. 348-363
Bibtex DOI: 10.1112/S0025579300007440Eisenbud, David and Bernd Sturmfels:
Finding sparse systems of parameters
In: Journal of pure and applied algebra,
94 (1994) 2, p. 143-157
Bibtex DOI: 10.1016/0022-4049(94)90029-9 ARXIV: http://arxiv.org/abs/alg-geom/9305010Onn, Shmuel and Bernd Sturmfels:
A note on lattice simplices and toric varieties
In: American journal of mathematics,
116 (1994) 5, p. 1337-1339
Bibtex DOI: 10.2307/2374948Onn, Shmuel and Bernd Sturmfels:
A quantitative Steinitz' theorem
In: Beiträge zur Algebra und Geometrie,
35 (1994) 1, p. 125-129
Bibtex LINK: http://www.emis.de/journals/BAG/vol.35/no.1/Sturmfels, Bernd:
Viro's theorem for complete intersections
In: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze,
21 (1994) 3, p. 377-386
Bibtex LINK: http://www.numdam.org/item?id=ASNSP_1994_4_21_3_377_0Sturmfels, Bernd:
On the Newton polytope of the resultant
In: Journal of algebraic combinatorics : an international journal,
3 (1994) 2, p. 207-236
Bibtex DOI: 10.1023/A:1022497624378Sturmfels, Bernd and Andrey V. Zelevinsky:
Multigraded resultants of Sylvester type
In: Journal of algebra,
163 (1994) 1, p. 115-127
Bibtex DOI: 10.1006/jabr.1994.1007Billera, Louis J. ; Gelfand, Izrail M. and Bernd Sturmfels:
Duality and minors of secondary polyhedra
In: Journal of combinatorial theory / B,
57 (1993) 2, p. 258-268
Bibtex DOI: 10.1006/jctb.1993.1020Bland, Robert G. ; Ko, Chun Wa and Bernd Sturmfels:
A nonextremal Camion basis
In: Linear algebra and its applications,
187 (1993), p. 195-199
Bibtex DOI: 10.1016/0024-3795(93)90135-BGritzmann, Peter and Bernd Sturmfels:
Minkowski addition of polytopes : computational complexity and applications to Gröbner
bases
In: SIAM journal on discrete mathematics,
6 (1993) 2, p. 246-269
Bibtex DOI: 10.1137/0406019Pedersen, Paul and Bernd Sturmfels:
Product formulas for resultants and Chow forms
In: Mathematische Zeitschrift,
214 (1993) 1, p. 377-396
Bibtex DOI: 10.1007/BF02572411Reeves, Alyson and Bernd Sturmfels:
A note on polynomial reduction
In: Journal of symbolic computation,
16 (1993) 3, p. 273-277
Bibtex DOI: 10.1006/jsco.1993.1045Sturmfels, Bernd and Andrey V. Zelevinsky:
Maximal minors and their leading terms
In: Advances in mathematics,
98 (1993) 1, p. 65-112
Bibtex DOI: 10.1006/aima.1993.1013Sturmfels, Bernd and Günter M. Ziegler:
Extension spaces of oriented matroids
In: Discrete and computational geometry,
10 (1993) 1, p. 23-45
Bibtex DOI: 10.1007/BF02573961Billera, Louis J. and Bernd Sturmfels:
Fiber polytopes
In: Annals of mathematics,
135 (1992) 3, p. 527-549
Bibtex DOI: 10.2307/2946575Kapranov, Mikhail M. ; Sturmfels, Bernd and Andrey V. Zelevinsky:
Chow polytopes and general resultants
In: Duke mathematical journal,
67 (1992) 1, p. 189-218
Bibtex DOI: 10.1215/S0012-7094-92-06707-XLogar, Alessandro and Bernd Sturmfels:
Algorithms for the Quillen-Suslin theorem
In: Journal of algebra,
145 (1992) 1, p. 231-239
Bibtex DOI: 10.1016/0021-8693(92)90189-SSturmfels, Bernd:
Asymptotic analysis of toric ideals
In: Memoirs of the faculty of science, Kyushu University. Series A : mathematics,
46 (1992) 2, p. 217-228
Bibtex DOI: 10.2206/kyushumfs.46.217Kapranov, Mikhail M. ; Sturmfels, Bernd and Andrey V. Zelevinsky:
Quotients of toric varieties
In: Mathematische Annalen,
290 (1991) 1, p. 643-655
Bibtex DOI: 10.1007/BF01459264Kleinschmidt, Peter and Bernd Sturmfels:
Smooth toric varieties with small Picard number are projective
In: Topology,
30 (1991) 2, p. 289-299
Bibtex DOI: 10.1016/0040-9383(91)90015-VRichter, Jürgen and Bernd Sturmfels:
On the topology and geometric construction of oriented matroids and convex polytopes
In: Transactions of the American Mathematical Society,
325 (1991) 1, p. 389-412
Bibtex DOI: 10.2307/2001676Sturmfels, Bernd:
Computational algebraic geometry of projective configurations
In: Journal of symbolic computation,
11 (1991) 5-6, p. 595-618
Bibtex DOI: 10.1016/S0747-7171(08)80121-6 LINK: https://www.ima.umn.edu/sites/default/files/389b.pdfSturmfels, Bernd:
Gröbner bases of toric varieties
In: Tohoku mathematical journal,
43 (1991) 2, p. 249-261
Bibtex DOI: 10.2748/tmj/1178227496Sturmfels, Bernd and Neil L. White:
Computing combinatorial decompositions of rings
In: Combinatorica,
11 (1991) 3, p. 275-293
Bibtex DOI: 10.1007/BF01205079Sturmfels, Bernd and Neil L. White:
Editorial
In: Journal of symbolic computation,
11 (1991) 5-6, p. 419-419
Bibtex DOI: 10.1016/S0747-7171(08)80112-5Sturmfels, Bernd and Walter Whiteley:
On the synthetic factorization of projectively invariant polynomials
In: Journal of symbolic computation,
11 (1991) 5-6, p. 439-453
Bibtex DOI: 10.1016/S0747-7171(08)80114-9Bayer, Margaret and Bernd Sturmfels:
Lawrence polytopes
In: Canadian journal of mathematics,
42 (1990) 1, p. 62-79
Bibtex DOI: 10.4153/CJM-1990-004-4Billera, Louis J. ; Filliman, Paul and Bernd Sturmfels:
Constructions and complexity of secondary polytopes
In: Advances in mathematics,
83 (1990) 2, p. 155-179
Bibtex DOI: 10.1016/0001-8708(90)90077-ZBokowski, Jürgen ; Richter, Jürgen and Bernd Sturmfels:
Nonrealizability proofs in computational geometry
In: Discrete and computational geometry,
5 (1990) 4, p. 333-350
Bibtex DOI: 10.1007/BF02187794Goodman, Jacob E. ; Pollack, Richard and Bernd Sturmfels:
The intrinsic spread of a configuration in Rd
In: Journal of the American Mathematical Society,
3 (1990) 3, p. 639-651
Bibtex DOI: 10.2307/1990931Gretenkort, Jörg ; Kleinschmidt, Peter and Bernd Sturmfels:
On the existence of certain smooth toric varieties
In: Discrete and computational geometry,
5 (1990) 3, p. 255-262
Bibtex DOI: 10.1007/BF02187789Sturmfels, Bernd:
Gröbner bases and Stanley decompositions of determinantal rings
In: Mathematische Zeitschrift,
205 (1990) 1, p. 137-144
Bibtex DOI: 10.1007/BF02571229Sturmfels, Bernd and Neil L. White:
Stanley decompositions of the bracket ring
In: Mathematica Scandinavica,
67 (1990) 2, p. 183-189
Bibtex LINK: www.jstor.org/stable/24492662Sturmfels, Bernd and Neil L. White:
All 11 3 and 12 3 -configurations are rational
In: Aequationes mathematicae,
39 (1990) 2-3, p. 254-260
Bibtex DOI: 10.1007/BF01833153Bokowski, Jürgen and Bernd Sturmfels:
An infinite family of minor-minimal nonrealizable 3-chirotopes
In: Mathematische Zeitschrift,
200 (1989) 4, p. 583-589
Bibtex DOI: 10.1007/BF01160956Havel, Timothy F. ; Sturmfels, Bernd and Neil L. White:
Proposal for a geometric algebra software package
In: ACM SIGSAM bulletin,
23 (1989) 1, p. 13-15
Bibtex DOI: 10.1145/66062.66064Jaggi, Beat ; Mani-Levitska, Peter ; Sturmfels, Bernd and Neil L. White:
Uniform oriented matroids without the isotopy property
In: Discrete and computational geometry,
4 (1989) 2, p. 97-100
Bibtex DOI: 10.1007/BF02187717Ljubic, Dragoslav ; Roudneff, Jean-Pierre and Bernd Sturmfels:
Arrangements of lines and pseudolines without adjacent triangles
In: Journal of combinatorial theory / A,
50 (1989) 1, p. 24-32
Bibtex DOI: 10.1016/0097-3165(89)90003-4Sturmfels, Bernd:
On the matroid stratification of Grassmann varieties, specialization of coordinates,
and a problem of N. White
In: Advances in mathematics,
75 (1989) 2, p. 202-211
Bibtex DOI: 10.1016/0001-8708(89)90037-6Sturmfels, Bernd:
Computing final polynomials and final syzygies using Buchberger's Gröbner bases
method
In: Results in mathematics,
15 (1989) 3-4, p. 351-360
Bibtex DOI: 10.1007/BF03322623Sturmfels, Bernd:
Dynamic versions of the Buchberger algorithm
In: RISC-Linz series : publications, reports (The Research Institute for Symbolic Computation),
1989 (1989), 89-16
Bibtex White, Neil L. and Bernd Sturmfels:
Gröbner bases and invariant theory
In: Advances in mathematics,
76 (1989) 2, p. 245-259
Bibtex DOI: 10.1016/0001-8708(89)90053-4Roudneff, Jean-Pierre and Bernd Sturmfels:
Simplicial cells in arrangements and mutations of oriented matroids
In: Geometriae dedicata,
27 (1988) 2, p. 153-170
Bibtex DOI: 10.1007/BF00151346Sturmfels, Bernd:
Neighborly polytopes and oriented matroids
In: European journal of combinatorics,
9 (1988) 6, p. 537-546
Bibtex DOI: 10.1016/S0195-6698(88)80050-7Sturmfels, Bernd:
Tridiagonalization of complex matrices and a problem of Longstaff
In: Linear algebra and its applications,
109 (1988), p. 165-166
Bibtex DOI: 10.1016/0024-3795(88)90207-8Sturmfels, Bernd:
Totally positive matrices and cyclic polytopes
In: Linear algebra and its applications,
107 (1988), p. 275-281
Bibtex DOI: 10.1016/0024-3795(88)90250-9Sturmfels, Bernd:
Some applications of affine Gale diagrams to polytopes with few vertices
In: SIAM journal on discrete mathematics,
1 (1988) 1, p. 121-133
Bibtex DOI: 10.1137/0401014Bokowski, Jürgen and Bernd Sturmfels:
Polytopal and nonpolytopal spheres an algorithmic approach
In: Israel journal of mathematics,
57 (1987) 3, p. 257-271
Bibtex DOI: 10.1007/BF02766213Sturmfels, Bernd:
Cyclic polytopes and d-order curves
In: Geometriae dedicata,
24 (1987) 1, p. 103-107
Bibtex DOI: 10.1007/BF00159750Sturmfels, Bernd:
Boundary complexes of convex polytopes cannot be characterized locally
In: The journal of the London Mathematical Society,
35 (1987) 2, p. 314-326
Bibtex DOI: 10.1112/jlms/s2-35.2.314Sturmfels, Bernd:
On the decidability of Diophantine problems in combinatorial geometry
In: Bulletin of the American Mathematical Society,
17 (1987) 1, p. 121-124
Bibtex DOI: 10.1090/S0273-0979-1987-15532-7Bokowski, Jürgen and Bernd Sturmfels:
On the coordinatization of oriented matroids
In: Discrete and computational geometry,
1 (1986) 4, p. 293-306
Bibtex DOI: 10.1007/BF02187702Sturmfels, Bernd:
Central and parallel projections of polytopes
In: Discrete mathematics,
62 (1986) 3, p. 315-318
Bibtex DOI: 10.1016/0012-365X(86)90220-7Publications in Books and Conference Proceedings
Kulkarni, Avinash ; Ren, Yue ; Sayyary Namin, Mahsa and Bernd Sturmfels:
Real space sextics and their tritangents
In: ISSAC '18 proceedings of the 43rd international symposium on symbolic and algebraic
computation ; New York, USA, July 16-19, 2018
Bibtex MIS-Preprint: 81/2017 DOI: 10.1145/3208976.3208977 ARXIV: https://arxiv.org/abs/1712.06274New York : ACM, 2018. - P. 247-254
Abo, Hirotachi ; Seigal, Anna and Bernd Sturmfels:
Eigenconfigurations of tensors
In: Algebraic and geometric methods in discrete mathematics / Heather A. Harrington... (eds.)
Providence, Rhode Island : American Mathematical Society, 2017. - P. 1-25
(Contemporary mathematics ; 685)
Bibtex DOI: 10.1090/conm/685/13717 ARXIV: http://arxiv.org/abs/1505.05729Kubjas, Kaie ; Parrilo, Pablo A. and Bernd Sturmfels:
How to flatten a soccer ball
In: Homological and computational methods in commutative algebra : dedicated to Winfried
Bruns on the occasion of his 70th birthday / Aldo Conca... (eds.)
Cham : Springer, 2017. - P. 141-162
(Springer INdAM series ; 20)
Bibtex DOI: 10.1007/978-3-319-61943-9_9 ARXIV: http://arxiv.org/abs/1606.02253Kukelova, Zuzana ; Kileel, Joe ; Sturmfels, Bernd and Tomas Pajdla:
A clever elimination strategy for efficient minimal solvers
In: 30th IEEE conference on computer vision and pattern recognition CVPR 2017, 21-26 July
2017 Honolulu, Hawaii : proceedings / Rama Chellappa... (eds.)
Bibtex DOI: 10.1109/CVPR.2017.384 ARXIV: https://arxiv.org/abs/1703.05289Piscataway, NJ : IEEE, 2017. - P. 3605-3614
Sturmfels, Bernd:
Fitness, apprenticeship, and polynomials
In: Combinatorial algebraic geometry : selected papers from the 2016 apprenticeship program / Bernd Sturmfels... (eds.)
New York : Springer, 2017. - P. 1-19
(Fields Institute communications ; 80)
Bibtex DOI: 10.1007/978-1-4939-7486-3_1 ARXIV: https://arxiv.org/abs/1612.03539Trager, Matthew ; Sturmfels, Bernd ; Canny, John ; Hebert, Martial and Jean Ponce:
General models for rational cameras and the case of two-slit projections
In: 30th IEEE conference on computer vision and pattern recognition CVPR 2017, 21-26 July
2017 Honolulu, Hawaii : proceedings / Rama Chellappa... (eds.)
Bibtex DOI: 10.1109/CVPR.2017.270 ARXIV: https://arxiv.org/abs/1612.01160Piscataway, NJ : IEEE, 2017. - P. 2520-2528
Améndola, Carlos ; Drton, Mathias and Bernd Sturmfels:
Maximum likelihood estimates for Gaussian mixtures are transcendental
In: Mathematical aspects of computer and information sciences : 6th international conference,
MACIS 2015, Berlin, Germany, November 11-13, 2015, revised selected papers / Ilias S. Kotsireas... (eds.)
Cham : Springer, 2016. - P. 579-590
(Lecture notes in computer science ; 9582)
Bibtex DOI: 10.1007/978-3-319-32859-1_49 ARXIV: http://arxiv.org/abs/1508.06958Bürgisser, Peter ; Kohn, Kathlén ; Lairez, Pierre and Bernd Sturmfels:
Computing the Chow variety of quadratic space curves
In: Mathematical aspects of computer and information sciences : 6th international conference,
MACIS 2015, Berlin, Germany, November 11-13, 2015, revised selected papers / Ilias S. Kotsireas... (eds.)
Cham : Springer, 2016. - P. 130-136
(Lecture notes in computer science ; 9582)
Bibtex DOI: 10.1007/978-3-319-32859-1_10 ARXIV: http://arxiv.org/abs/1508.07219Draisma, Jan ; Horobet, Emil ; Ottaviani, Giorgio ; Sturmfels, Bernd and Rekha R. Thomas:
The Euclidean distance degree
In: SNC 2014 : proceedings of the 2014 symposium on symbolic-numeric computation : July
28-31, 2014, Shanghai, China / Stephen M. Watt (ed.)
Bibtex DOI: 10.1145/2631948.2631951New York : ACM, 2014. - P. 9-16
Huh, June and Bernd Sturmfels:
Likelihood geometry
In: Combinatorial algebraic geometry : lecture notes from the CIME-CIRM summer school
held in Levico Terme, June 10-15, 2013 / Aldo Conca... (eds.)
New York : Springer, 2014. - P. 63-117
(Lecture notes in mathematics ; 2108)
Bibtex DOI: 10.1007/978-3-319-04870-3_3 ARXIV: http://arxiv.org/abs/1305.7462Sturmfels, Bernd:
Maximum likelihood for matrices with rank constraints : [invited talk abstract]
In: ISSAC '14 proceedings of the 39th international symposium on symbolic and algebraic
computation ; Kobe, Japan July 23-25, 2014 / Katsusuke Nabeshima (ed.)
Bibtex DOI: 10.1145/2608628.2627490New York : ACM, 2014. - P. 17-17
Chan, Melody and Bernd Sturmfels:
Elliptic curves in honeycomb form
In: Algebraic and combinatorial aspects of tropical geometry / Erwan Brugallé... (eds.)
Providence, R.I. : American Mathematical Society, 2013. - P. 87-107
(Contemporary mathematics ; 589)
Bibtex DOI: 10.1090/conm/589/11743 ARXIV: http://arxiv.org/abs/1203.2356Rostalski, Philipp and Bernd Sturmfels:
Dualities
In: Semidefinite optimization and convex algebraic geometry / Grigoriy Blekherman... (eds.)
Philadelphia : Society for Industrial and Applied Mathematics, 2013. - P. 203-249
(MOS-SIAM series on optimization ; 13)
Bibtex Plaumann, Daniel ; Sturmfels, Bernd and Cynthia Vinzant:
Computing linear matrix representations of Helton-Vinnikov curves
In: Mathematical methods in systems, optimization, and control : Festschrift in honor
of J. William Helton / Harry Dym... (eds.)
Basel : Springer, 2012. - P. 259-277
(Operator theory : advances and applications ; 222)
Bibtex DOI: 10.1007/978-3-0348-0411-0_19 ARXIV: http://arxiv.org/abs/1011.6057Ranestad, Kristian and Bernd Sturmfels:
The convex hull of a variety
In: Notions of positivity and the geometry of polynomials / Petter Brändén... (eds.)
Basel : Birkhäuser, 2011. - P. 331-344
(Trends in mathematics)
Bibtex DOI: 10.1007/978-3-0348-0142-3_18 ARXIV: http://arxiv.org/abs/1004.3018Riegler, Erwin ; Morgenshtern, Veniamin I. ; Durisi, Giuseppe ; Lin, Shaowei ; Sturmfels, Bernd and Helmut Bölcskei:
Noncoherent SIMO pre-log via resolution of singularities
In: IEEE international symposium on information theory proceedings (ISIT) 2011 : July
31-August 5, 2011 in St. Petersburg, Russia
Bibtex DOI: 10.1109/ISIT.2011.6033909 ARXIV: http://arxiv.org/abs/1105.6009Piscataway, NY : IEEE, 2011. - P. 2020-2024
Cueto, Maria Angélica ; Morton, Jason and Bernd Sturmfels:
Geometry of the restricted Boltzmann machine
In: Algebraic methods in statistics and probability : volume 2 / Marlos A. G. Viana... (eds.)
Providence, R.I. : American Mathematical Society, 2010. - P. 135-153
(Contemporary mathematics ; 516)
Bibtex DOI: 10.1090/conm/516/10172 ARXIV: http://arxiv.org/abs/0908.4425Sturmfels, Bernd:
Open problems in algebraic statistics
In: Emerging applications of algebraic geometry / Mihai Putinar... (eds.)
New York : Springer, 2009. - P. 351-363
(The IMA volumes in mathematics and its applications ; 149)
Bibtex DOI: 10.1007/978-0-387-09686-5_10 ARXIV: http://arxiv.org/abs/0707.4558Nie, Jiawang ; Parrilo, Pablo A. and Bernd Sturmfels:
Semidefinite representation of the \({k}\)-ellipse
In: Algorithms in algebraic geometry / Alicia Dickenstein... (eds.)
New York : Springer, 2008. - P. 117-132
(The IMA volumes in mathematics and its applications ; 146)
Bibtex DOI: 10.1007/978-0-387-75155-9_7 ARXIV: http://arxiv.org/abs/math/0702005Sturmfels, Bernd and Josephine Yu:
Tropical implicitization and mixed fiber polytopes
In: Software for algebraic geometry / Michael E. Stillman... (eds.)
New York : Springer, 2008. - P. 111-131
(The IMA volumes in mathematics and its applications ; 148)
Bibtex DOI: 10.1007/978-0-387-78133-4_7 ARXIV: http://arxiv.org/abs/0706.0564Fotiou, Ioannis A. ; Rostalski, Philipp ; Sturmfels, Bernd and Manfred Morari:
An algebraic geometry approach to nonlinear parametric optimization in control
In: Proceedings of the 2006 american control conference : Minneapolis, Minnesota, USA,
June 14-16, 2006
Bibtex DOI: 10.1109/ACC.2006.1657280 ARXIV: http://arxiv.org/abs/math/0509288New York : IEEE, 2006. - P. 3618-3623
Morton, Jason ; Pachter, Lior ; Shiu, Anne ; Sturmfels, Bernd and Oliver Wienand:
Geometry of rank tests
In: Proceedings of the third european workshop on probabilistic graphical models : Prague,
Czech Republic, September 12-15, 2006 / Milan Studeny... (eds.)
Bibtex ARXIV: http://arxiv.org/abs/math/0605173 LINK: http://www.utia.cas.cz/pgm06_proceedingsPrague : Agentura Action M, 2006
Develin, Mike ; Santos, Francisco and Bernd Sturmfels:
On the rank of a tropical matrix
In: Combinatorial and computational geometry / Jacob Eli Goodman... (eds.)
Cambridge : Cambridge University Press, 2005. - P. 213-242
(Mathematical sciences research institute publications ; 52)
Bibtex ARXIV: http://arxiv.org/abs/math/0312114Eriksson, Nicholas ; Ranestad, Kristian ; Sturmfels, Bernd and Seth Sullivant:
Phylogenetic algebraic geometry
In: Projective varieties with unexpected properties : a volume in memory of Giuseppe Veronese
; proceedings of the international conference 'Varieties with Unexpected Properties',
Siena, Italy, June 8-13, 2004 / Ciro Ciliberto... (eds.)
Bibtex DOI: 10.1515/9783110199703.237 ARXIV: http://arxiv.org/abs/math/0407033Berlin : de Gruyter, 2005. - P. 237-255
Pachter, Lior and Bernd Sturmfels:
Statistics [chapter 1]
In: Algebraic statistics for computational biology / Lior Pachter... (eds.)
Bibtex DOI: 10.1017/CBO9780511610684.004Cambridge : Cambridge University Press, 2005. - P. 3-42
Pachter, Lior and Bernd Sturmfels:
Computation [chapter 2]
In: Algebraic statistics for computational biology / Lior Pachter... (eds.)
Bibtex DOI: 10.1017/CBO9780511610684.005Cambridge : Cambridge University Press, 2005. - P. 43-84
Pachter, Lior and Bernd Sturmfels:
Algebra [chapter 3]
In: Algebraic statistics for computational biology / Lior Pachter... (eds.)
Bibtex DOI: 10.1017/CBO9780511610684.006Cambridge : Cambridge University Press, 2005. - P. 85-124
Pachter, Lior and Bernd Sturmfels:
Preface
In: Algebraic statistics for computational biology / Lior Pachter... (eds.)
Bibtex DOI: 10.1017/CBO9780511610684.001Cambridge : Cambridge University Press, 2005
Richter-Gebert, Jürgen ; Sturmfels, Bernd and Thorsten Theobald:
First steps in tropical geometry
In: Idempotent mathematics and mathematical physics : international workshop February
3-10, 2003 Erwin Schrödinger international institute for mathematical physics
Vienna, Austria / Grigory L. Litvinov... (eds.)
Providence, R.I. : American Mathematical Society, 2005. - P. 289-317
(Contemporary mathematics ; 377)
Bibtex DOI: 10.1090/conm/377/06998 ARXIV: http://arxiv.org/abs/math/0306366Sturmfels, Bernd:
Algebraic recipes for integer programming
In: Trends in Optimization / Serkan Hosten... (eds.)
Providence, R.I. : American Mathematical Society, 2004. - P. 99-113
(Proceedings of symposia in applied mathematics ; 61)
Bibtex DOI: 10.1090/psapm/061/2104733 ARXIV: https://arxiv.org/abs/math/0310194Parrilo, Pablo A. and Bernd Sturmfels:
Minimizing polynomial functions
In: Algorithmic and quantitative real algebraic geometry : proceedings of the DIMACS workshop
on algorithmic and quantitative aspects of real algebraic geometry in mathematics
and computer science, DIMACS Center, March 12-16, 2001 / Saugata Basu... (eds.)
Providence, R.I. : American Mathematical Society, 2003. - P. 83-99
(Series in discrete mathematics and theoretical computer science ; 60)
Bibtex ARXIV: https://arxiv.org/abs/math/0103170Geiger, Dan ; Meek, Christopher and Bernd Sturmfels:
Factorization of discrete probability distributions
In: Uncertainty in artificial intelligence : proceedings of the eighteenth conference
(2002) ; August 1-4, 2002, University of Alberta, Edmonton / Adnan Darwiche (ed.)
Bibtex ARXIV: http://de.arxiv.org/abs/1301.0568San Francisco : Morgan Kaufmann, 2002. - P. 162-169
Smith, Gregory G. and Bernd Sturmfels:
Teaching the geometry of schemes
In: Computations in algebraic geometry with Macaulay 2 / David Eisenbud... (eds.)
Berlin : Springer, 2002. - P. 55-70
(Algorithms and computation in mathematics ; 8)
Bibtex DOI: 10.1007/978-3-662-04851-1_4 ARXIV: http://de.arxiv.org/abs/math/0003033Stillman, Michael E. ; Sturmfels, Bernd and Rekha R. Thomas:
Algorithms for the toric Hilbert scheme
In: Computations in algebraic geometry with Macaulay 2 / David Eisenbud... (eds.)
Berlin : Springer, 2002. - P. 179-214
(Algorithms and computation in mathematics ; 8)
Bibtex DOI: 10.1007/978-3-662-04851-1_8 ARXIV: https://arxiv.org/abs/math/0010130Sturmfels, Bernd:
Ideals, varieties and Macaulay 2
In: Computations in algebraic geometry with Macaulay 2 / David Eisenbud... (eds.)
Berlin : Springer, 2002. - P. 3-15
(Algorithms and computation in mathematics ; 8)
Bibtex DOI: 10.1007/978-3-662-04851-1_1Sturmfels, Bernd:
Gröbner bases of abelian matrix groups
In: Symbolic computation : solving equations in algebra, geometry, and engineering / Edward L. Green... (eds.)
Providence, R.I. : American Mathematical Society, 2001. - P. 141-143
(Contemporary mathematics ; 286)
Bibtex DOI: 10.1090/conm/286/04760Miller, Ezra and Bernd Sturmfels:
Monomial ideals and planar graphs
In: Applied algebra, algebraic algorithms and error-correcting codes : 13th international
symposium, AAECC-13 Honolulu, Hawaii, USA, November 15-19, 1999 proceedings / Marc Fossorier... (eds.)
Berlin : Springer, 1999. - P. 19-28
(Lecture notes in computer science ; 1719)
Bibtex DOI: 10.1007/3-540-46796-3_3Sturmfels, Bernd:
The Co-Scarf resolution
In: Commutative algebra, algebraic geometry, and computational methods : proceedings of
the conference on algebraic geometry, commutative algebra, and computation, Hanoi,
Vietnam, 1996 / David Eisenbud (ed.)
Bibtex Singapore : Springer, 1999. - P. 315-320
Diaconis, Persi ; Eisenbud, David and Bernd Sturmfels:
Lattice walks and primary decomposition
In: Mathematical essays in honor of Gian-Carlo Rota / Bruce Eli Sagan... (eds.)
Boston : Birkhäuser, 1998. - P. 173-193
(Progress in mathematics ; 161)
Bibtex DOI: 10.1007/978-1-4612-4108-9_8Sturmfels, Bernd:
Introduction to resultants
In: Applications of computational algebraic geometry : lectures presented at the American
Mathematical Society ; short course held in San Diego, CA, January 6-7, 1997 / David A. Cox... (eds.)
Providence, R.I. : American Mathematical Society, 1998. - P. 25-39
(Proceedings of symposia in applied mathematics ; 53)
Bibtex DOI: 10.1090/psapm/053/1602347Sturmfels, Bernd and Nobuki Takayama:
Gröbner bases and hypergeometric functions
In: Gröbner bases and applications : [Proceedings of the conference 33 years of
Gröbner bases] / Bruno Buchberger... (eds.)
Cambridge : Cambridge University Press, 1998. - P. 246-258
(London Mathematical Society lecture note series ; 251)
Bibtex Sturmfels, Bernd:
Equations defining toric varieties
In: Algebraic geometry Santa Cruz 1995
Providence, R.I. : American Mathematial Society, 1997. - P. 437-449
(Proceedings of symposia in pure mathematics ; 62.2)
Bibtex DOI: 10.1090/pspum/062.2/1492542 ARXIV: https://arxiv.org/abs/alg-geom/9610018Cattani, Eduardo ; Dickenstein, Alicia and Bernd Sturmfels:
Computing multidimensional residues
In: Algorithms in algebraic geometry and applications / Laureano Gonzalez-Vega... (eds.)
Basel : Birkhäuser, 1996. - P. 135-164
(Progress in mathematics ; 143)
Bibtex DOI: 10.1007/978-3-0348-9104-2_8 ARXIV: https://arxiv.org/abs/alg-geom/9404011v1Diaconis, Persi ; Graham, Ronald L. and Bernd Sturmfels:
Primitive partition identities
In: Combinatorics, Paul Erdos is eighty (Vol. 2) / Dézso Miklós... (eds.)
Budapest : János Bolyai Mathematical Society, 1996. - P. 173-192
(Bolyai Society Mathematical studies ; 2)
Bibtex LINK: https://oeis.org/A007343/a007343.pdfPedersen, Paul and Bernd Sturmfels:
Mixed monomial bases
In: Algorithms in algebraic geometry and applications / Laureano Gonzalez-Vega... (eds.)
Basel : Birkhäuser, 1996. - P. 307-316
(Progress in mathematics ; 143)
Bibtex DOI: 10.1007/978-3-0348-9104-2_15Dalbec, John and Bernd Sturmfels:
Introduction to Chow forms
In: Invariant methods in discrete and computational geometry : proceedings of the Curacao
conference, 13-17 June, 1994 / Neil L. White (ed.)
Bibtex DOI: 10.1007/978-94-015-8402-9_2Dordrecht : Kluwer Academic, 1995. - P. 37-58
Hosten, Serkan and Bernd Sturmfels:
GRIN : an implementation of Gröbner bases for integer programming
In: Integer programming and combinatorial optimization : 4th International IPCO Conference
Copenhagen, Denmark, May 29-31, 1995 : proceedings / Egon Balas (ed.)
Berlin : Springer, 1995. - P. 267-276
(Lecture notes in computer science ; 920)
Bibtex DOI: 10.1007/3-540-59408-6_57Sturmfels, Bernd:
On the number of real roots of a sparse polynomial system
In: Hamiltonian and gradient flows, algorithms and control / Anthony Bloch (ed.)
Providence, R.I. : American Mathematical Society, 1994. - P. 137-143
(Fields Institute communications ; 3)
Bibtex Sturmfels, Bernd and Josephine Yu:
Minimal polynomials and sparse resultants
In: Zero-dimensional schemes : proceedings of the international conference held in Ravello,
June 8- 3, 1992 / Ferruccio Orecchia (ed.)
Bibtex Berlin : de Gruyter, 1994. - P. 317-324
Sturmfels, Bernd:
Sparse elimination theory
In: Computational algebraic geometry and commutative algebra : proceedings of a conference
held at Cortona, Italy, June 17-21, 1991 / David Eisenbud (ed.)
Cambridge : Cambridge University Press, 1993. - P. 264-298
(Symposia mathematica ; 34)
Bibtex Kleinschmidt, Peter ; Schwartz, Niels and Bernd Sturmfels:
Unimodular fans, linear codes, and toric manifolds
In: Discrete and computational geometry : papers from the DIMACS special year / Jacob Eli Goodman... (eds.)
Providence, R. I. : American Mathematical Society, 1991. - P. 179-186
(DIMACS series in discrete mathematics and theoretical computer science ; 6)
Bibtex Rota, Gian-Carlo and Bernd Sturmfels:
Introduction to invariant theory in superalgebras
In: Invariant theory and tableaux : [workshop on invariant theory and tableaux held at
the IMA on March 21-25, 1988] / Dennis Stanton (ed.)
New York : Springer, 1990. - P. 1-35
(The IMA volumes in mathematics and its applications ; 19)
Bibtex Goodman, Jacob E. ; Pollack, Richard and Bernd Sturmfels:
Coordinate representation of order types requires exponential storage
In: Proceedings of the twenty-first annual ACM symposium on theory of computing : Seattle,
1989
Bibtex DOI: 10.1145/73007.73046New York : ACM, 1989. - P. 405-410
Sturmfels, Bernd:
Aspects of computational synthetic geometry : I. Algorithmic coordinatization of matroids
In: Computer-aided geometric reasoning : workshop, 22-26 juin 1987, INRIA Sophia-Antipolis
(France) : volume 1. / Henry H. Crapo (ed.)
Bibtex Le Chesnay : INRIA, 1987. - P. 57-86
Bokowski, Jürgen and Bernd Sturmfels:
Reell realisierbare orientierte Matroide
In: Diskrete Strukturen, algebraische Methoden und Anwendungen : 2. Sommerschule Diskrete
Strukturen, Bayreuth, 1985 / Adalbert Kerber (ed.)
Bayreuth : Universitat Bayreuth, 1986. - P. 1-13
(Bayreuther mathematische Schriten ; 21)
Bibtex Preprints
Breiding, Paul ; Sturmfels, Bernd and Sascha Timme:
3264 conics in a second
Bibtex MIS-Preprint: 24/2019 ARXIV: https://arxiv.org/abs/1902.05518
Duarte, Eliana ; Marigliano, Orlando and Bernd Sturmfels:
Discrete statistical models with rational maximum likelihood estimator
Bibtex MIS-Preprint: 29/2019 ARXIV: https://arxiv.org/abs/1903.06110
Joswig, Michael ; Panizzut, Marta and Bernd Sturmfels:
The Schläfli fan
Bibtex MIS-Preprint: 41/2019 ARXIV: https://arxiv.org/abs/1905.11951
Sturmfels, Bernd ; Uhler, Caroline and Piotr Zwiernik:
Brownian motion tree models are toric
Bibtex MIS-Preprint: 26/2019 ARXIV: https://arxiv.org/abs/1902.09905
Baletti, Gabriele ; Sturmfels, Bernd and Marta Panizzut:
K3 polytopes and their quartic surfaces
Bibtex MIS-Preprint: 40/2018 ARXIV: https://arxiv.org/abs/1806.02236
Cifuentes, Diego ; Ranestad, Kristian ; Sturmfels, Bernd and Madeleine Weinstein:
Voronoi cells of varieties
Bibtex MIS-Preprint: 98/2018 ARXIV: https://arxiv.org/abs/1811.08395
Kohn, Kathlén ; Shapiro, Boris and Bernd Sturmfels:
Moment varieties of measures on polytopes
Bibtex MIS-Preprint: 50/2018 ARXIV: https://arxiv.org/abs/1807.10258
Löhne, Andreas ; Ciripoi, Daniel ; Kaihnsa, Nidhi and Bernd Sturmfels:
Computing convex hulls of trajectories
Bibtex MIS-Preprint: 89/2018 ARXIV: https://arxiv.org/abs/1810.03547
Robeva, Elina ; Sturmfels, Bernd ; Tran, Ngoc Mai and Caroline Uhler:
Maximum likelihood estimation for totally positive log-concave densities
Bibtex MIS-Preprint: 42/2018 ARXIV: https://arxiv.org/abs/1806.10120
Lin, Bo ; Sturmfels, Bernd ; Tang, Xiaoxian and Ruriko Yoshida:
Appendix for 'Convexity in tree spaces'
Agarwal, Sameer ; Lee, Hon-Leung ; Sturmfels, Bernd and Rekha R. Thomas:
Certifying the existence of epipolar matrices
Lin, Shaowei ; Oeding, Luke and Bernd Sturmfels:
Electric network synthesis
Schweighofer, Markus ; Sturmfels, Bernd and Rekha R. Thomas:
Convex algebraic geometry
De Loera, Jesús A. and Bernd Sturmfels:
Counting network flows
Sturmfels, Bernd:
The geometry of A-graded algebras
Billera, Louis J. ; Kapranov, Mikhail M. and Bernd Sturmfels:
On a conjecture of Baues in the theory of loop spaces
Crapo, Henry H. ; Havel, Timothy F. ; Sturmfels, Bernd ; Whiteley, Walter and Neil L. White:
Symbolic computations in geometry
Sturmfels, Bernd:
An algorithmic proof of the Quillen-Suslin theorem
Sturmfels, Bernd:
Simplicial polytopes without the isotopy property
Sturmfels, Bernd and Neil L. White:
Constructing uniform oriented matroids without the isotopy property
Sturmfels, Bernd and Neil L. White:
Rational realizations of 113- and 123- configurations
Sturmfels, Bernd and Walter Whiteley:
On the synthetic factorization of homogeneous invariants
Sturmfels, Bernd:
Applications of final polynomials and final syzygies
Bokowski, Jürgen and Bernd Sturmfels:
Programmsystem zur Realisierung orientierter Matroide
Academic Theses
Sturmfels, Bernd:
Oriented matroids and combinatorial convex geometry
Dissertation, Technische Hochschule Darmstadt, 1987
Bibtex Books
Smith, Gregory G. and Bernd Sturmfels (eds.):
Combinatorial algebraic geometry : selected papers from the 2016 apprenticeship program
New York : Springer, 2017. - VIII, 390 p.
(Fields Institute communications ; 80)
ISBN 978-1-4939-7486-3 ISBN 978-1-4939-7485-6
Bibtex DOI: 10.1007/978-1-4939-7486-3Maclagan, Diane and Bernd Sturmfels:
Introduction to tropical geometry
Providence, R.I. : American Mathematical Society, 2015. - XII, 363 p.
(Graduate studies in mathematics ; 161)
ISBN 978-0-8218-5198-2
Bibtex Conca, Aldo ; Di Rocco, Sandra ; Draisma, Jan ; Huh, June ; Sturmfels, Bernd and Filippo Viviani (eds.):
Combinatorial algebraic geometry : lecture notes from the CIME-CIRM summer school
held in Levico Terme, June 10-15, 2013
Cham : Springer, 2014. - VII, 239 p.
(Lecture notes in mathematics ; 2108)
ISBN 978-3-319-04870-3 ISBN 978-3-319-04869-7
Bibtex DOI: 10.1007/978-3-319-04870-3Avramov, Luchezar L. ; Green, Mark ; Huneke, Craig ; Smith, Karen E. and Bernd Sturmfels (eds.):
Trends in commutative algebra : [Based on lectures presented at the MSRI introductory
workshop on commutative algebra held at the Mathematical Sciences Research Institute,
Berkeley, CA, USA, September 9-13, 2002]
Reprint of the 2004 hardback edition. - New York : Cambridge University Press, 2011. - X, 254 p.
(Mathematical sciences research institute publications ; 51)
ISBN 978-0-521-16872-4 ISBN 978-0-511-15945-9
Bibtex Drton, Mathias ; Sturmfels, Bernd and Seth Sullivant:
Lectures on algebraic statistics
Boston, MA : Birkhäuser, 2009. - VIII, 171 p.
(Oberwolfach seminars ; 39)
ISBN 978-3-7643-8904-8 ISBN 978-3-7643-8905-5
Bibtex DOI: 10.1007/978-3-7643-8905-5Sturmfels, Bernd:
Algorithms in invariant theory
Second edition. - Wien : Springer, 2008. - 197 p.
(Texts and monographs in symbolic computation)
ISBN 978-3-211-77416-8 ISBN 978-3-211-77417-5
Bibtex DOI: 10.1007/978-3-211-77417-5Miller, Ezra ; Reiner, Victor and Bernd Sturmfels (eds.):
Geometric combinatorics : lectures from the graduate summer school held in Park City,
UT, 2004
Providence, R.I. : American Mathematical Society, 2007. - XII, 691 p.
(IAS/Park City mathematics series ; 13)
ISBN 978-0-8218-3736-8 ISBN 0-8218-3736-2
Bibtex Miller, Ezra and Bernd Sturmfels:
Combinatorial commutative algebra
New York : Springer, 2005. - XIV, 417 p.
(Graduate texts in mathematics ; 227)
ISBN 978-0-387-22356-8 ISBN 978-0-387-27103-3 ISBN 0-387-22356-8
Bibtex DOI: 10.1007/b138602Pachter, Lior and Bernd Sturmfels (eds.):
Algebraic statistics for computational biology
Cambridge : Cambridge University Press, 2005. - XII, 420 p.
ISBN 0-521-85700-7 ISBN 978-0-521-85700-0
Bibtex DOI: 10.1017/CBO9780511610684Avramov, Luchezar L. ; Green, Mark ; Huneke, Craig ; Smith, Karen E. and Bernd Sturmfels (eds.):
Trends in commutative algebra : [Based on lectures presented at the MSRI introductory
workshop on commutative algebra held at the Mathematical Sciences Research Institute,
Berkeley, CA, USA, September 9-13, 2002]
New York : Cambridge University Press, 2004. - X, 254 p.
(Mathematical sciences research institute publications ; 51)
ISBN 978-0-521-83195-6 ISBN 978-0-521-16872-4 ISBN 0-521-83195-4 ISBN 0-511-15945-5
Bibtex Eisenbud, David ; Grayson, Daniel R. ; Stillman, Michael E. and Bernd Sturmfels (eds.):
Computations in algebraic geometry with Macaulay 2
Berlin : Springer, 2002. - XIII, 329 p.
(Algorithms and computation in mathematics ; 8)
ISBN 978-3-642-07592-6 ISBN 978-3-662-04851-1 ISBN 3-540-42230-7
Bibtex DOI: 10.1007/978-3-662-04851-1Sturmfels, Bernd:
Solving systems of polynomial equations
Providence, R.I. : American Mathematical Society, 2002. - VIII, 152 p.
(CBMS regional conference series in mathematics ; 97)
ISBN 978-0-8218-3251-6 ISBN 978-1-4704-2457-2 ISBN 0-8218-3251-4
Bibtex DOI: 10.1090/cbms/097Saito, Mutsumi ; Sturmfels, Bernd and Nobuki Takayama:
Gröbner deformations of hypergeometric differential equations
Berlin : Springer, 2000. - VIII, 254 p.
(Algorithms and computation in mathematics ; 6)
ISBN 978-3-642-08534-5 ISBN 978-3-662-04112-3
Bibtex DOI: 10.1007/978-3-662-04112-3Björner, Anders ; Las Vergnas, Michel ; Sturmfels, Bernd ; White, Neil L. and Günter M. Ziegler (eds.):
Oriented matroids
Second edtion. - Cambridge : Cambridge University Press, 1999. - XII, 548 p.
(Encyclopedia of mathematics and its applications ; 46)
ISBN 0-521-77750-x ISBN 978-0-521-77750-6 ISBN 978-0-511-89363-6
Bibtex Cox, David A. and Bernd Sturmfels (eds.):
Applications of computational algebraic geometry : lectures presented at the American
Mathematical Society ; short course held in San Diego, CA, January 6-7, 1997
Providence, R.I. : American Mathematical Society, 1998. - IX, 172 p.
(Proceedings of symposia in applied mathematics ; 53)
ISBN 978-0-8218-0750-7 ISBN 978-0-8218-9268-8 ISBN 0-8218-0750-1
Bibtex DOI: 10.1090/psapm/053Sturmfels, Bernd:
Gröbner bases and convex polytopes
Providence, R.I. : American Mathematical Society, 1996. - XI, 162 p.
(University lecture series ; 8)
ISBN 0-8218-0487-1 ISBN 978-1-4704-9787-1 ISBN 978-0-8218-0487-2
Bibtex DOI: 10.1090/ulect/008Björner, Anders ; Las Vergnas, Michel ; Sturmfels, Bernd ; White, Neil L. and Günter M. Ziegler (eds.):
Oriented matroids
Cambridge : Cambridge University Press, 1993. - XII, 516 p.
(Encyclopedia of mathematics and its applications ; 46)
ISBN 0-521-41836-4
Bibtex Hilbert, David ; Sturmfels, Bernd and Reinhard Laubenbacher:
Theory of algebraic invariants
Cambridge : Cambridge University Press, 1993. - XIV, 191 p.
(Cambridge mathematical library)
ISBN 0-521-44903-0 ISBN 0-521-44457-8
Bibtex Sturmfels, Bernd:
Algorithms in invariant theory
Wien : Springer, 1993. - 197 p.
(Texts and monographs in symbolic computation)
ISBN 0-387-82445-6 ISBN 3-211-82445-6
Bibtex Gritzmann, Peter and Bernd Sturmfels (eds.):
Applied geometry and discrete mathematics : the Victor Klee Festschrift
Providence, R. I. : American Mathematical Society, 1991. - XL, 608 p.
(DIMACS series in discrete mathematics and theoretical computer science ; 4)
ISBN 0-8218-6593-5 ISBN 0-89791-385-x
Bibtex Bokowski, Jürgen and Bernd Sturmfels:
Computational synthetic geometry
Berlin : Springer, 1989. - 168 p.
(Lecture notes in mathematics ; 1355)
ISBN 978-3-540-50478-8 ISBN 978-3-540-46013-8
Bibtex DOI: 10.1007/BFb0089253Sturmfels, Bernd:
Computational synthetic geometry