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MiS Preprint
93/2018
Flag matroids: algebra and geometry
Amanda Cameron, Rodica Dinu, Mateusz Michałek and Tim Seynnaeve
Matroids are ubiquitous in modern combinatorics. As discovered by Gelfand, Goresky, MacPherson and Serganova there is a beautiful connection between matroid theory and the geometry of Grassmannians: realizable matroids correspond to torus orbits in Grassmannians. Further, as observed by Fink and Speyer general matroids correspond to classes in the $K$-theory of Grassmannians. This yields in particular a geometric description of the Tutte polynomial.
In this review we describe all these constructions in detail, and moreover we generalise some of them to polymatroids. More precisely, we study the class of flag matroids and their relations to flag varieties. In this way, we obtain an analogue of the Tutte polynomial for flag matroids.
flag matroids, Tutte polynomial, K-theory of flag varieties
Related publications
inBook
2022
Repository Open Access
Amanda Cameron, Rodica Dinu, Mateusz Michałek and Tim Seynnaeve
Flag matroids : algebra and geometry
In: Interactions with lattice polytopes : Magdeburg, Germany, September 2017 / Alexander M. Kasprzyk... (eds.) Cham : Springer, 2022. - pp. 73-114 (Springer proceedings in mathematics and statistics ; 386)
