Séminaire Lotharingien de Combinatoire, B78c (2020), 17 pp.
Spencer Backman and Matthias Lenz
A Convolution Formula for Tutte Polynomials of Arithmetic Matroids
and Other Combinatorial Structures
Abstract.
In this note we generalize the convolution formula for the Tutte polynomial of
Kook, Reiner, and Stanton and of Etienne and 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.
Received: April 1, 2017.
Accepted: March 14, 2019.
Final Version: January 26, 2020.
The following versions are available: