Equivalence Classes of Colorings
Abstract
For any link and for any modulus we introduce an equivalence relation on the set of non-trivial m-colorings of the link (an m-coloring has values in Z/mZ). Given a diagram of the link, the equivalence class of a non-trivial m-coloring is formed by each assignment of colors to the arcs of the diagram that is obtained from the former coloring by a permutation of the colors in the arcs which preserves the coloring condition at each crossing. This requirement implies topological invariance of the equivalence classes. We show that for a prime modulus the number of equivalence classes depends on the modulus and on the rank of the coloring matrix (with respect to this modulus).
Cite
@article{arxiv.1208.0993,
title = {Equivalence Classes of Colorings},
author = {Jun Ge and Slavik Jablan and Louis H. Kauffman and Pedro Lopes},
journal= {arXiv preprint arXiv:1208.0993},
year = {2017}
}
Comments
This is the version accepted for publication of the article formerly entitled "Equivalence Classes of Colorings: the Topological Viewpoint"