Haruspicy 3: The directed bond-animal generating function is not D-finite
Abstract
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.
Cite
@article{arxiv.math/0408054,
title = {Haruspicy 3: The directed bond-animal generating function is not D-finite},
author = {Andrew Rechnitzer},
journal= {arXiv preprint arXiv:math/0408054},
year = {2007}
}
Comments
20 pages and 10 figures. Submitted to Journal of Combinatorial Theory Series A