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

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Spencer Backman , Matthias Lenz ·

YOU? · · 2016 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1602.02664 · OA: W2257136508

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.