For any link and for any modulus m 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).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc103-0-2,
author = {Jun Ge and Slavik Jablan and Louis H. Kauffman and Pedro Lopes},
title = {Equivalence classes of colorings},
journal = {Banach Center Publications},
volume = {102},
year = {2014},
pages = {63-76},
zbl = {1316.57012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc103-0-2}
}
Jun Ge; Slavik Jablan; Louis H. Kauffman; Pedro Lopes. Equivalence classes of colorings. Banach Center Publications, Tome 102 (2014) pp. 63-76. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc103-0-2/