Removing Colors 2k, 2k-1, and k

TL;DR

This paper proves that for links with non-trivial colorings in certain prime moduli, there exist equivalent colorings avoiding specific colors, expanding understanding of link colorings in knot theory.

Contribution

It introduces a method to find non-trivial colorings that exclude particular colors for links with prime moduli greater than 7.

Findings

Existence of non-trivial colorings avoiding colors 2k, 2k-1, and k

Applicable to links with prime moduli greater than 7

Advances the theory of link colorings in knot theory

Abstract

We prove that if a link admits non-trivial (2k+1)-colorings, with prime 2k+1>7, it also admits non-trivial (2k+1)-colorings not involving colors 2k, 2k-1, nor k.