Affiliation:
1. Center for Mathematical Analysis, Geometry and Dynamical Systems, Portugal
2. Department of Mathematics, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
Abstract
This article concerns exact results on the minimum number of colors of a Fox coloring over the integers modulo r, of a link with non-null determinant.Specifically, we prove that whenever the least prime divisor of the determinant of such a link and the modulus r is 2, 3, 5, or 7, then the minimum number of colors is 2, 3, 4, or 4 (respectively) and conversely.We are thus led to conjecture that for each prime p there exists a unique positive integer, mp, with the following property. For any link L of non-null determinant and any modulus r such that p is the least prime divisor of the determinant of L and the modulus r, the minimum number of colors of L modulo r is mp.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
12 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. The palette numbers of torus knots;Journal of Knot Theory and Its Ramifications;2017-09
2. Minimal sufficient sets of colors and minimum number of colors;Journal of Knot Theory and Its Ramifications;2017-08
3. The 6- and 8-palette numbers of links;Topology and its Applications;2017-05
4. The minimum number of Fox colors modulo 13 is 5;Topology and its Applications;2017-02
5. Fox coloring and the minimum number of colors;Involve, a Journal of Mathematics;2017-01-01