Virtual links with finite medial bikei. (May 2019)

• Record Type: Journal Article
• Authors: Chien, Julien; Nelson, Sam
• Is Part Of: Journal of symbolic computation. Volume 92(2019)
• Page Start: 211
• Page End: 221
• Publication Date: 2019-05
• Subjects: Bikei -- Involutory biquandles -- Medial bikei -- Finite presentations; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.04.015
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We consider the question of which virtual knots have finite fundamental medial bikei. We describe and implement an algorithm for completing a presentation matrix of a medial bikei to an operation table, determining both the cardinality and isomorphism class of the fundamental medial bikei, each of which are link invariants. As an example, we compute the fundamental medial bikei for all of the prime virtual knots with up to four classical crossings as listed in the knot atlas.