Haruspicy 3: The directed bond-animal generating function is not D-finite

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While directed site-animals have been solved on several lattices, directed bond-animals remain unsolved on any non-trivial lattice. In this paper we demonstrate that the anisotropic generating function of directed bond-animals on the square lattice is fundamentally different from that of directed site-animals in that it is not differentiably finite. We also extend this result to directed bond-animals on hypercubic lattices. This indicates that directed bond-animals are unlikely to be solved by similar methods to those used in the solution of directed site-animals. It also implies that a solution cannot by conjectured using computer packages such as GFUN or differential approximants.
20 pages and 10 figures. Submitted to Journal of Combinatorial Theory Series A

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Combinatorics, Statistical Mechanics, Mathematical Physics, 05A15, 82B20

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http://salesiana.dossiersoluciones.com/handle/123456789/72105

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0408054
 http://arxiv.org/abs/math/0408054

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arXiv