Stavros Garoufalidis and Martin Loebl.
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.
Key words: Colored Jones function, permanents, weight systems, random walks.
Notes: 13 pages, 12 figures.