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

Simple item page
dc.creatorRechnitzer, Andrew
dc.date2004-08-04
dc.date.accessioned2026-07-07T05:11:00Z
dc.date.available2026-07-07T05:11:00Z
dc.descriptionWhile 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.
dc.description20 pages and 10 figures. Submitted to Journal of Combinatorial Theory Series A
dc.identifierhttps://arxiv.org/abs/math/0408054
dc.identifierhttp://arxiv.org/abs/math/0408054
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72105
dc.subjectCombinatorics
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.subject05A15, 82B20
dc.titleHaruspicy 3: The directed bond-animal generating function is not D-finite
dc.typetext

Files

Collections

arXiv