Alex Fink, David E Speyer
Published 2010-04-14, updated 2010-08-26Version 2
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.
Comments: v2: added a starting point for combinatorialists in Section 2.4, + minor changes
K-classes of delta-matroids and equivariant localization
Parallel connections and bundles of arrangements
The ring $\mathrm{M}_{8k+4}(\mathbb{Z}_2)$ is nil-clean of index four
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