Minimal Numbers of Fox Colors and Quandle Cocycle Invariants of Knots

2009/05/27 by Masahico Saito, Saito, Masahico
Mathematics · #57M25 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M25

paper · pdf · doi:10.48550/arxiv.0905.4486

arxiv created 2009/05/27 · openalex publication_date 2009/05/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Relations will be described between the quandle cocycle invariant and the minimal number of colors used for non-trivial Fox colorings of knots and links. In particular, a lower bound for the minimal number is given in terms of the quandle cocycle invariant.

Related

• The minimum number of Fox colors modulo 13 is 5
• Extensions of Quandles and Cocycle Knot Invariants
• Quandles at Finite Temperatures II
• On the minimum number of Fox Colorings of Knots
• Minimum numbers of Dehn colors of knots and symmetric local biquandle cocycle invariants