Chromatic polynomial, q-binomial counting and colored Jones function
نویسندگان
چکیده
منابع مشابه
Chromatic Polynomial, Colored Jones Function and Q-binomial Counting
Abstract. We define a q-chromatic function on graphs, list some of its properties and provide some formulas in the class of general chordal graphs. Then we relate the q-chromatic function to the colored Jones function of knots. This leads to a curious expression of the colored Jones function of a knot diagram K as a ’defected chromatic operator’ applied to a power series whose coefficients are ...
متن کاملThe colored Jones function is q–holonomic
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 ...
متن کاملAsymptotics of the Colored Jones Polynomial and the A-polynomial
The N-colored Jones polynomial JK (N) is a quantum invariant which is defined based on the N-dimensional irreducible representation of the quantum group Uq(sl(2)). Motivated by Volume Conjecture raised by Kashaev [16], it was pointed out that the colored Jones polynomial at a specific value should be related to the hyperbolic volume of knot complement [21]. As another example of the knot invari...
متن کاملThe Colored Jones Polynomial and the A-polynomial of Knots
We study relationships between the colored Jones polynomial and the A-polynomial of a knot. The AJ conjecture (of Garoufalidis) that relates the colored Jones polynomial and the A-polynomial is established for a large class of two-bridge knots, including all twist knots. We formulate a weaker conjecture and prove that it holds for all two-bridge knots. Along the way we also calculate the Kauffm...
متن کاملColored Jones Polynomials with Polynomial Growth
Abstract. The volume conjecture and its generalizations say that the colored Jones polynomial corresponding to the N-dimensional irreducible representation of sl(2;C) of a (hyperbolic) knot evaluated at exp(c/N) grows exponentially with respect to N if one fixes a complex number c near 2π √ −1. On the other hand if the absolute value of c is small enough, it converges to the inverse of the Alex...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2007
ISSN: 0001-8708
DOI: 10.1016/j.aim.2006.09.001