Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial

Abstract

We study the head and tail of the colored Jones polynomial while focusing mainly on alternating links. Various ways to compute the colored Jones polynomial for a given link give rise to combinatorial identities for those power series. We further show that the head and tail functions only depend on the reduced checkerboard graphs of the knot diagram. Moreover the class of head and tail functions of prime alternating links forms a monoid.

27 pages

Cited by in corpus (9)

• A $q$-series identity via the ${\mathfrak{sl}}_3$ colored Jones polynomials for the $(2,2m)$-torus link
• A trivial tail homology for non $A$-adequate links
• Khovanov homology of a unicolored B-adequate link has a tail
• Pretzel Knots and q-Series
• Colored Jones polynomials without tails
• An Efficient Algorithm to Compute the Colored Jones Polynomial
• Foundations of the Colored Jones Polynomial of singular knots
• Twist formulas for one-row colored $A_2$ webs and ${\mathfrak{sl}}_3$ tails of $(2,2m)$-torus links
• Twist Regions and Coefficients Stability of the Colored Jones Polynomial