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arXiv · 2508.00561

Multivariate Tutte polynomials of semimatroids

Houshan Fu
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Abstract

We introduce and investigate multivariate Tutte polynomials, dichromatic polynomials, subset-corank polynomials, size-corank polynomials, and rank generating polynomials of semimatroids, which generalize the corresponding polynomial invariants of graphs and matroids. We primarily establish their deletion-contraction recurrences, basis activities expansions, and various convolution identities. These findings naturally extend Kook-Reiner-Stanton's convolution formula and Kung's convolution-multiplication identities for the Tutte polynomials of graphs and matroids to semimatroids.

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Houshan Fu. 2025-08-01. Multivariate Tutte polynomials of semimatroids. https://arxiv.org/abs/2508.00561

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