# Equivalence classes of colorings

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

Banach Center Publications (2014)

- Volume: 103, Issue: 1, page 63-76
- ISSN: 0137-6934

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topJun Ge, et al. "Equivalence classes of colorings." Banach Center Publications 103.1 (2014): 63-76. <http://eudml.org/doc/281811>.

@article{JunGe2014,

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).},

author = {Jun Ge, Slavik Jablan, Louis H. Kauffman, Pedro Lopes},

journal = {Banach Center Publications},

keywords = {links; colourings; equivalence classes of colourings},

language = {eng},

number = {1},

pages = {63-76},

title = {Equivalence classes of colorings},

url = {http://eudml.org/doc/281811},

volume = {103},

year = {2014},

}

TY - JOUR

AU - Jun Ge

AU - Slavik Jablan

AU - Louis H. Kauffman

AU - Pedro Lopes

TI - Equivalence classes of colorings

JO - Banach Center Publications

PY - 2014

VL - 103

IS - 1

SP - 63

EP - 76

AB - 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).

LA - eng

KW - links; colourings; equivalence classes of colourings

UR - http://eudml.org/doc/281811

ER -

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