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Equivalence classes of colorings

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Ge J., Jablan S., Kauffman L., Lopes P.

Banach Center Publications

2014

tom 103

nr 1

63-76

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).

Ograniczanie wyników

1 Banach Center Publications

1 Ge J.

1 Jablan S.

1 Kauffman L.

1 Lopes P.

1 2014

Wyniki wyszukiwania

Equivalence classes of colorings