K-classes for matroids and equivariant localization

By Alex Fink, David E. Speyer. 2010

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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. R´ esum´ e. ` A chaque matronous associons une classe dans la K-thde la grassmannienne. Nous ´

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/23d60fb1a27e6643cde5502e6ab09e1190e6cb0c

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Citations in the corpus

Coxeter submodular functions and deformations of Coxeter permutahedra (2019, background): “See [7] for their implications for polytopes, [16] for applications to matroids, and [42] for a combinatorial formula for the dimension of the space of parallel redrawings of a generic embedding of a graph.”
Matroid Theory for Algebraic Geometers (2014, background): “There is a diagram (borrowed from [36]) of morphisms forgetting various stages of the flags:”
Patch ideals and Peterson varieties (2011, background): “ocally trivial ﬁbration. Thus, local features of Ycan, in principle, be studied by considering X=ρ−1(Y)⊆ GL n/B. Remark 2.7. If X⊆ G/P, then take X∩ gB−P/Pto be an Xpatch. See work of A. FinkD.Speyer [FinSpe10]where theequivariant K-localizations of TxintheGrassmannian are connected to matroid invar”