On the Counting of Colored Tangles
Mathematical Physics
2007-05-23 v2 High Energy Physics - Theory
Combinatorics
math.MP
Abstract
The connection between matrix integrals and links is used to define matrix models which count alternating tangles in which each closed loop is weighted with a factor n, i.e. may be regarded as decorated with n possible colors. For n=2, the corresponding matrix integral is that recently solved in the study of the random lattice six-vertex model. The generating function of alternating 2-color tangles is provided in terms of elliptic functions, expanded to 16-th order (16 crossings) and its asymptotic behavior is given.
Cite
@article{arxiv.math-ph/0002020,
title = {On the Counting of Colored Tangles},
author = {P. Zinn-Justin and J. -B. Zuber},
journal= {arXiv preprint arXiv:math-ph/0002020},
year = {2007}
}
Comments
16 pages. revised: counting up to 16 crossings