On the Counting of Colored Tangles

Details On the Counting of Colored Tangles On the Counting of Colored Tangles

2000-02-08

arxiv.org/abs/math-ph/0002020v2

Journal of Knot Theory and its Ramifications 9 (2000) 1127--1141

Physics

Mathematical Physics

16 pages. revised: counting up to 16 crossings

Scientific paper

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.

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