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On the Counting of Colored Tangles

P. Zinn-Justin·J. -B. Zuber
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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.

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P. Zinn-Justin, J. -B. Zuber. 2000-06-15. On the Counting of Colored Tangles. https://arxiv.org/abs/math-ph/0002020

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