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arXiv · 2401.06869

Categorical valuative invariants of polyhedra and matroids

Ben Elias·Dane Miyata·Nicholas Proudfoot·Lorenzo Vecchi
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Abstract

We introduce the notion of a categorical valuative invariant of polyhedra or matroids, in which alternating sums of numerical invariants are replaced by split exact sequences in an additive category. We provide categorical lifts of a number of valuative invariants of matroids, including the Poincare polynomial, the Chow and augmented Chow polynomials, and certain two-variable extensions of the Kazhdan--Lusztig polynomial and Z-polynomial. These lifts allow us to perform calculations equivariantly with respect to automorphism groups of matroids.

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Ben Elias, Dane Miyata, Nicholas Proudfoot, Lorenzo Vecchi. 2024-01-12. Categorical valuative invariants of polyhedra and matroids. https://arxiv.org/abs/2401.06869

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