Random walks and the colored Jones function

2002/03/01 by Stavros Garoufalidis, Garoufalidis, Stavros, Martin Loebl +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #Topological and Geometric Data Analysis #math.GT #math.QA

paper · pdf · doi:10.48550/arxiv.math/0203012

AMS-LaTeX, 13 pages with 12 figures

arxiv created 2002/03/01 · openalex publication_date 2002/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight system. We give two curious formulas for the weight system of a colored Jones function: one in terms of the permanent of a matrix associated to a chord diagram, and another in terms of counting paths of intersecting chords.

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