Colorings and flows on CW complexes, Tutte quasi-polynomials and arithmetic matroids

Abstract

In this note we provide a higher-dimensional analogue of Tutte's celebrated theorem on colorings and flows of graphs, by showing that the theory of arithmetic Tutte polynomials and quasi-polynomials encompasses invariants defined for CW complexes by Beck-Breuer-Godkin-Martin and Duval-Klivans-Martin. Furthermore, we answer a question by Bajo-Burdick-Chmutov, concerning the modified Tutte-Krushkal-Renhardy polynomials defined by these authors: to this end, we prove that the product of two arithmetic multiplicity functions on a matroid is again an arithmetic multiplicity function.

9 pages; proof of Theorem 1 corrected

References in corpus (1)

• Splines, lattice points, and arithmetic matroids

Cited by in corpus (3)

• A convolution formula for Tutte polynomials of arithmetic matroids and other combinatorial structures
• Answering Two OPAC Problems Involving Banff Quivers
• An equivalent formulation of chromatic quasi-polynomials