Colorings and flows on CW complexes, Tutte quasi-polynomials and arithmetic matroids
Combinatorics
2016-05-17 v3 Algebraic Topology
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.
Keywords
Cite
@article{arxiv.1602.04307,
title = {Colorings and flows on CW complexes, Tutte quasi-polynomials and arithmetic matroids},
author = {Emanuele Delucchi and Luca Moci},
journal= {arXiv preprint arXiv:1602.04307},
year = {2016}
}
Comments
9 pages; proof of Theorem 1 corrected