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

2016/02/08 by Backman, Spencer, Lenz, Matthias · 2 citations
#05C10 #05C21 #05C31 #52C35 #Combinatorics (math.CO) #FOS: Mathematics #Primary: 05B35 #Secondary: 05C15

paper · doi:10.48550/arxiv.1602.02664

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.

Cited by

• Multivariate Tutte polynomials of semimatroids
• Characteristic polynomials of semimatroids and their connections to matroids, hyperplane arrangements and graph colorings

Related

• Convolution formulas for multivariate arithmetic Tutte polynomials
• A convolution formula for the Tutte polynomial
• Convolution-multiplication identities for Tutte polynomials of matroids
• Colorings and flows on CW complexes, Tutte quasi-polynomials and arithmetic matroids
• The multivariate arithmetic Tutte polynomial