Random Walks And The Colored Jones Function

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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Correspondence to Stavros Garoufalidis*.

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* S. G. was partially supported by an NSF and by an Israel-US BSF grant.

† M. L. was partly supported by GAUK 158 grant and by the Project LN00A056 of the Czech Ministry of Education.

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Garoufalidis*, S., Loebl†, M. Random Walks And The Colored Jones Function. Combinatorica 25, 651–671 (2005). https://doi.org/10.1007/s00493-005-0041-3

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Mathematics Subject Classification (2000):

  • 57N10
  • 57M25