Equivalence Classes of Colorings

Jun Ge; Slavik Jablan; Louis H. Kauffman; Pedro Lopes

doi:10.4064/bc103-0-2

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arXiv · 1208.0993

Equivalence Classes of Colorings

Jun Ge·Slavik Jablan·Louis H. Kauffman·Pedro Lopes

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Abstract

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).

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BibTeX RIS

Jun Ge, Slavik Jablan, Louis H. Kauffman, Pedro Lopes. 2014-05-07. Equivalence Classes of Colorings. https://doi.org/10.4064/bc103-0-2

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