Research ArticleNo Access

Presentations of diquandles and diquandle coloring invariants for solid torus knots and links

Jieon Kim

Department of Mathematics, Pusan National University, Busan 46241, Republic of Korea

E-mail Address: jieonkim@pusan.ac.kr

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Sang Youl Lee

Department of Mathematics, Pusan National University, Busan 46241, Republic of Korea

E-mail Address: sangyoul@pusan.ac.kr

Corresponding author.

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Mohd Ibrahim Sheikh

Department of Mathematics, Graduate School of Natural Sciences, Pusan National University, Busan 46241, Republic of Korea

E-mail Address: ibrahimsheikh@pusan.ac.kr

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https://doi.org/10.1142/S021821652350102XCited by:0 (Source: Crossref)

Abstract

A diquandle is a set equipped with two quandle operations interacting via a kind of distributive laws which come from Reidemeister moves on dichromatic links. This algebraic systems provide coloring invariants for dichromatic links. In this paper, we give explicit constructions of free diquandles and diquandle presentations, and then discuss Tietze transformations for the diquandle presentations. We also introduce the fundamental diquandles for dichromatic links. Particularly, we describe the fundamental diquandles and diquandle counting invariants for knots and links in the solid torus via annulus diagrams. We append the tables of diquandles and dikei’s of orders $\leq 5$ .

Keywords:

AMSC: 57K10, 57K12

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