Minimum numbers of Dehn colors of knots and symmetric local biquandle cocycle invariants

TL;DR

This paper introduces a method to determine the minimum number of Dehn colors for knots using symmetric local biquandle cocycle invariants, revealing knots distinguished by these minimum numbers.

Contribution

It presents a novel approach connecting Dehn coloring minimal numbers with symmetric local biquandle cocycle invariants, answering open questions from prior research.

Findings

Existence of knots distinguished by minimum Dehn color numbers

Method to evaluate minimum Dehn colors using cocycle invariants

Answers to open questions from previous work

Abstract

In this paper, we give a method to evaluate minimum numbers of Dehn colors for knots by using symmetric local biquandle cocycle invariants. We give answers to some questions arising as a consequence of our previous paper [6]. In particular, we show that there exist knots which are distinguished by minimum numbers of Dehn colors.