Work

Entropic Niebrzydowski tribrackets

Year: 2025

Type: article

Abstract: In this paper, we introduce the notion of entropic Niebrzydowski tribrackets or just entropic tribrackets, analogous to entropic (also known as abelian or medial) quandles and biquandles. We show that if [Formula: see text] is a finite entropic tribracket then for any tribracket [Formula: see text], the homset [Formula: see text] (and in particular, for any oriented link [Formula: see text], the homset [Formula: see text]) also has the structure of an entropic tribracket. This operation yields a product on the category of entropic tribrackets; we compute the operation table for entropic tribrackets of small cardinality and prove a few results. We conjecture that this structure can be used to distinguish links which have the same counting invariant with respect to a chosen entropic coloring tribracket [Formula: see text].

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s0218216525500397

Authors: Jieon Kim, Sam Nelson

Institutions: Pusan National University, Claremont McKenna College

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Simons Foundation, National Research Foundation, National Research Foundation of Korea, Ministry of Education, Science and Technology

Awards: G6817113029, G8254858323, G8611440762