K-theoretic Tutte polynomials of morphisms of matroids

Dinu, Rodica; Eur, Christopher; Seynnaeve, Tim (2021). K-theoretic Tutte polynomials of morphisms of matroids. Journal of combinatorial theory. Series A, 181, p. 105414. Elsevier 10.1016/j.jcta.2021.105414

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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.

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