A one-variable bracket polynomial for some Turk's head knots

2018/07/13 by Franck Ramaharo, Ramaharo, Franck
Mathematics · #05A19 #57M25 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1807.05256

openalex publication_date 2018/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the Kauffman bracket polynomial of the three-lead Turk's head, the chain sinnet and the figure-eight chain shadow diagrams. Each of these knots can in fact be constructed by repeatedly concatenating the same 3-tangle, respectively, then taking the closure. The bracket is then evaluated by expressing the state diagrams of the concerned 3-tangle by means of the Kauffman monoid diagram's elements.

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