Random Walks And The Colored Jones Function
نویسندگان
چکیده
منابع مشابه
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 diagra...
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We initiate a study of random walks on undirected graphs with colored edges. In our model, a sequence of colors is speciied before the walk begins, and it dictates the color of edge to be followed at each step. We give tight upper and lower bounds on the expected cover time of a random walk on an undirected graph with colored edges. We show that, in general, graphs with two colors have exponent...
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A function of several variables is called holonomic if, roughly speaking, it is determined from finitely many of its values via finitely many linear recursion relations with polynomial coefficients. Zeilberger was the first to notice that the abstract notion of holonomicity can be applied to verify, in a systematic and computerized way, combinatorial identities among special functions. Using a ...
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The colored Jones function of a knot is a sequence of Laurent polynomials. It was shown by TTQ. Le and the author that such sequences are q-holonomic, that is, they satisfy linear q-difference equations with coefficients Laurent polynomials in q and qn. We show from first principles that q-holonomic sequences give rise to modules over a q-Weyl ring. Frohman-Gelca-LoFaro have identified the latt...
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A model of random walk on knot diagrams is used to study the Alexander polynomial and the colored Jones polynomial of knots. In this context, the inverse of the Alexander polynomial of a knot plays the role of an Ihara-Selberg zeta function of a directed weighted graph, counting with weights cycles of random walk on a 1-string link whose closure is the knot in question. The colored Jones polyno...
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2005
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-005-0041-3