Random Walks And The Colored Jones Function |
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Authors: | Stavros Garoufalidis Martin Loebl? |
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Institution: | (1) School of Mathematics Georgia, Institute of Technology, Atlanta, GA 30332-0160, USA;(2) KAM MFF UK and ITI Charles University, Malostranske n.25, 118 00 Praha 1, Czech Republic |
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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.
Electronic supplementary material to this article is available at and is accessible to authorized users.
* 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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Keywords: | 57N10 57M25 |
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