Random walks and the colored Jones function

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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.
AMS-LaTeX, 13 pages with 12 figures

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Geometric Topology, Quantum Algebra

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http://salesiana.dossiersoluciones.com/handle/123456789/63472

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0203012
 http://arxiv.org/abs/math/0203012

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arXiv