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MiS Preprint

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.

MSC Codes:
05B35, 52B40, 14M15, 14M25, 19E08
flag matroids, Tutte polynomial, K-theory of flag varieties

Related publications

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)