%0 Journal Article
%T Haruspicy 3: The directed bond-animal generating function is not D-finite
%A Andrew Rechnitzer
%J Mathematics
%D 2004
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0408054v1