A lower bound on minimal number of colors for links

TL;DR

This paper establishes a logarithmic lower bound on the minimal number of colors needed for effective n-colorings of links with non-zero determinant, advancing understanding of link colorings in knot theory.

Contribution

It introduces a new lower bound of 1 + log2 n for the minimal number of colors in effective n-colorings of links with non-zero determinant.

Findings

Minimal number of colors grows at least logarithmically with n.

Provides a theoretical bound applicable to all links with non-zero determinant.

Enhances the mathematical understanding of link colorings in knot theory.

Abstract

We show that the minimal number of colors for all effective $n$-colorings of a link with non-zero determinant is at least $1+\log_2 n$.