K-theoretic Tutte polynomials of morphisms of matroids

We generalize the Tutte polynomial of a matroid to a morphism of matroids via the K-theory of flag varieties. We introduce two different generalizations, and demonstrate that each has its own merits, where the trade-off is between the ease of combinatorics and geometry. One generalization recovers t...

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Bibliographic Details
Published in:arXiv.org 2021-01
Main Authors: Dinu, Rodica, Eur, Christopher, Seynnaeve, Tim
Format: Article
Language:English
Subjects:
Combinatorial analysis
Flags
Polynomials
Online Access:Get full text
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Summary:We generalize the Tutte polynomial of a matroid to a morphism of matroids via the K-theory of flag varieties. We introduce two different generalizations, and demonstrate that each has its own merits, where the trade-off is between the ease of combinatorics and geometry. One generalization recovers the Las Vergnas Tutte polynomial of a morphism of matroids, which admits a corank-nullity formula and a deletion-contraction recursion. The other generalization does not, but better reflects the geometry of flag varieties.
ISSN:2331-8422