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arXiv · 1602.02664

A convolution formula for Tutte polynomials of arithmetic matroids and other combinatorial structures

Spencer Backman·Matthias Lenz
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Abstract

In this note we generalize the convolution formula for the Tutte polynomial of Kook-Reiner-Stanton and Etienne-Las Vergnas to a more general setting that includes both arithmetic matroids and delta-matroids. As corollaries, we obtain new proofs of two positivity results for pseudo-arithmetic matroids and a combinatorial interpretation of the arithmetic Tutte polynomial at infinitely many points in terms of arithmetic flows and colorings. We also exhibit connections with a decomposition of Dahmen-Micchelli spaces and lattice point counting in zonotopes.

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Spencer Backman, Matthias Lenz. 2016-02-08. A convolution formula for Tutte polynomials of arithmetic matroids and other combinatorial structures. https://arxiv.org/abs/1602.02664

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