Elsevier

Advances in Mathematics

Volume 211, Issue 2, 1 June 2007, Pages 546-565
Advances in Mathematics

Chromatic polynomial, q-binomial counting and colored Jones function

https://doi.org/10.1016/j.aim.2006.09.001Get rights and content
Under an Elsevier user license
open archive

Abstract

We define a q-chromatic function and q-dichromate on graphs and compare it with existing graph functions. Then we study in more detail the class of general chordal graphs. This is partly motivated by the graph isomorphism problem. Finally 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 chromatic operator applied to a power series whose coefficients are linear combinations of long chord diagrams. Chromatic operators are directly related to weight systems by the work of Chmutov, Duzhin, Lando and Noble, Welsh.

MSC

primary
05A30
secondary
57N10

Keywords

Chromatic polynomial
Tutte polynomial
Quantum binomial identity
Colored Jones function

Cited by (0)