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K-classes of matroids and equivariant localization

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arxiv 1004.2403 v2 pith:RXNQ5MW5 submitted 2010-04-14 math.CO math.AG

Alex Fink , David E Speyer This is my paper · ORCID
classification math.COmath.AG
keywords classequivariantlocalizationmatroidsresultswereassociateauthor
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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.

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  1. Graph theoretic properties of Speyer's matroid polynomial $g_M(t)$

    math.CO 2025-06 accept novelty 7.0 of 10

    For graphic and cographic matroids, the derivative g'_M(-1) equals (-1)^{c(M)-1} c(M), and computational data suggests many new properties of the coefficient N2.

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