K-classes of matroids and equivariant localization
Combinatorics
2019-12-19 v2 Algebraic Geometry
Abstract
To every matroid, we associate a class in the K-theory of the Grassmannian. We study this class using the method of equivariant localization. In particular, we provide a geometric interpretation of the Tutte polynomial. We also extend results of the second author concerning the behavior of such classes under direct sum, series and parallel connection and two-sum; these results were previously only established for realizable matroids, and their earlier proofs were more difficult.
Cite
@article{arxiv.1004.2403,
title = {K-classes of matroids and equivariant localization},
author = {Alex Fink and David E Speyer},
journal= {arXiv preprint arXiv:1004.2403},
year = {2019}
}
Comments
v2: added a starting point for combinatorialists in Section 2.4, + minor changes