Knots and Coxeter Groups

2025/03/13 by D. L. Burke, Geoffrey Cuff-Chartrand, Burke, Dylan +7
Mathematics · #28A80 #57K10 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2503.10785

openalex publication_date 2025/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study knots created by galleries in the affine Coxeter complex of type \widewedgeB3. We bound the stick number by 40 and prove that the smallest length of threefold rotationally symmetric trefoils is 42. We construct explicit galleries that knot as 9₃5, 9₄0, 9₄1 and 9₄7 in a way that has threefold rotational symmetry. We explain the construction of these galleries for 9₄7 carefully. We conclude with three questions inspired by this work.

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