Cameron, Amanda; Dinu, Rodica; Michałek, Mateusz; Seynnaeve, Tim (9 June 2022). Flag Matroids: Algebra and Geometry. In: Kasprzyk, Alexander M.; Nill, Benjamin (eds.) Interactions with Lattice Polytopes. Springer Proceedings in Mathematics & Statistics: Vol. 386 (pp. 73-114). Springer, Cham 10.1007/978-3-030-98327-7_4
Full text not available from this repository. (Request a copy)Matroids are ubiquitous in modern combinatorics. As discovered by Gel’fand, Goresky, MacPherson and Serganova there is a beautiful connection between matroid theory and the geometry of Grassmannians: representable 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.
Item Type: |
Conference or Workshop Item (Paper) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Seynnaeve, Tim |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
2194-1017 |
ISBN: |
978-3-030-98326-0 |
Series: |
Springer Proceedings in Mathematics & Statistics |
Publisher: |
Springer, Cham |
Language: |
English |
Submitter: |
Zarif Ibragimov |
Date Deposited: |
14 Mar 2023 10:51 |
Last Modified: |
14 Mar 2023 23:27 |
Publisher DOI: |
10.1007/978-3-030-98327-7_4 |
URI: |
https://boris.unibe.ch/id/eprint/180011 |
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