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Knots and Permutations

Jaime Rangel-Mondragón
Organization: Universidad Autonoma de Querétaro
Department: Facultad de Informatica
Journal / Anthology

Instituto Tecnologio y de Estudios Superiores de Monterrey. Research Report
Year: 1996

A relationship between the menage problem and the study of alternating knots is developed following the ideas of Tait and Gilbert. Use is made of Burnside's theorem to count the equivalent classes of knots derived from considering equivalence of permutations under conjugation. Concrete implementations are offered using the programming language Mathematica.

*Mathematics > Algebra > Group Theory
*Mathematics > Discrete Mathematics > Combinatorics
*Mathematics > Topology

menage permutations, Burnside's theorem, knots, alternating knots, equivalence, group theory, combinatorics