Work

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

Year: 2026

Type: article

Abstract: This is the second paper which discusses minimum numbers of “region” colors for knots, while minimum numbers of arc colors are well-studied, where the first one is our previous paper [E. Matsudo, K. Oshiro and G. Yamagishi, Minimum numbers of Dehn colors of knots and [Formula: see text]-palette graphs, Adv. Appl. Math. 173 (2026) 102995]. 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 [E. Matsudo, K. Oshiro and G. Yamagishi, Minimum numbers of Dehn colors of knots and [Formula: see text]-palette graphs, Adv. Appl. Math. 173 (2026) 102995]. In particular, we show that there exist knots which are distinguished by minimum numbers of Dehn colors.

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s0218216526500525

Authors: Eri Matsudo, Kanako Oshiro, Gaishi Yamagishi

Institutions: Nihon University, Sophia University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Award: 絡み目に関わる代数系の整理と絡み目不変量の再定式化