Equivalence classes of colorings

Jun 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 -