Equivalence classes of colorings

• Autorzy: Jun Ge , Slavik Jablan , Louis H. Kauffman , Pedro Lopes
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 57M27: Invariants of knots and 3-manifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2014
• Tom: 103
• Numer: 1
• Strony: 63-76

Daty

wydano

2014

Twórcy

autor

Jun Ge

• School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, P. R. China

autor

Slavik Jablan

• The Mathematical Institute, Knez Mihailova 36, P.O. Box 367, 11001, Belgrade, Serbia

autor

Louis H. Kauffman

• Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S. Morgan St., Chicago, IL 60607-7045, USA

autor

Pedro Lopes

• Center for Mathematical Analysis, Geometry and Dynamical Systems, Department of Mathematics, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisbon, Portugal

Identyfikatory

DOI

10.4064/bc103-0-2