Haruspicy 2: The anisotropic generating function of self-avoiding polygons not D-finite

Details Haruspicy 2: The anisotropic generating function of self-avoiding polygons not D-finite Haruspicy 2: The anisotropic generating function of self-avoiding polygons not D-finite

2004-06-23

arxiv.org/abs/math/0406450v2

Mathematics

Combinatorics

28 pages and 15 figures. Accepted for publication in Journal of Combinatorial Theory Series A

Scientific paper

We prove that the anisotropic generating function of self-avoiding polygons is not a D-finite function - proving a conjecture of Guttmann and Enting. This result is also generalised to self-avoiding polygons on hypercubic lattices. Using the haruspicy techniques developed in an earlier paper we are also prove the form of the coefficients of the anisotropic generating function, which was first conjectured by Guttmann and Enting.

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