Loading...
Enumerating Colorings, Tensions and Flows in Cell Complexes
Beck, Matthias Breuer, Felix Godkin, Logan Martin, Jeremy L.
Beck, Matthias
Breuer, Felix
Godkin, Logan
Martin, Jeremy L.
Citations
Altmetric:
Abstract
We study quasipolynomials enumerating proper colorings, nowhere-zero tensions, and nowhere-zero flows in an arbitrary CW-complex X, generalizing the chromatic, tension and flow polynomials of a graph. Our colorings, tensions and flows may be either modular (with values in Z/kZZ/kZ for some k) or integral (with values in {−k+1,…,k−1}{−k+1,…,k−1}). We obtain deletion–contraction recurrences and closed formulas for the chromatic, tension and flow quasipolynomials, assuming certain unimodularity conditions. We use geometric methods, specifically Ehrhart theory and inside-out polytopes, to obtain reciprocity theorems for all of the aforementioned quasipolynomials, giving combinatorial interpretations of their values at negative integers as well as formulas for the numbers of acyclic and totally cyclic orientations of X.
Description
this is the author's final draft. Copyright 2014 Elsevier.
Date
2014-02
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Collections
Research Projects
Organizational Units
Journal Issue
Keywords
Graph, Cell complex, Chromatic polynomial, Combinatorial reciprocity, Flows, Tensions
Citation
Beck, Matthias, Felix Breuer, Logan Godkin, and Jeremy L. Martin. "Enumerating Colorings, Tensions and Flows in Cell Complexes." Journal of Combinatorial Theory, Series A 122 (2014): 82-106. doi:10.1016/j.jcta.2013.10.002.