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

Research paper by Andrew Rechnitzer

Indexed on: 15 Apr '05Published on: 15 Apr '05Published in: Mathematics - Combinatorics



Abstract

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.