2000/02/29 by P. Zinn-Justin, J. -B. Zuber
Physics and Astronomy · Mathematics · #math-ph #hep-th #math.CO #math.MP
published as Journal of Knot Theory and its Ramifications 9 (2000) 1127--1141 · 16 pages. revised: counting up to 16 crossings
arxiv created 2000/06/15 · arxiv updated 2009/11/30
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.