Random walks and the colored Jones function

Stavros Garoufalidis; Martin Loebl

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arXiv · math/0203012

Random walks and the colored Jones function

Stavros Garoufalidis·Martin Loebl

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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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Stavros Garoufalidis, Martin Loebl. 2002-03-01. Random walks and the colored Jones function. https://arxiv.org/abs/math/0203012

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