Haruspicy 3：有向键动物generating function不是D-有限的
Haruspicy 3: The directed bond-animal generating function is not D-finite
摘要：
虽然有向site-animals已经解决了几个格，有向bond-animals仍然没有解决任何非平凡格。本文证明了正方形格点上有向键动物的各向异性母函数与有向位动物的母函数的根本不同之处在于它不是可微有限的。我们也将这个结果推广到超立方格上的有向键动物。这表明定向键动物不太可能通过与定向位点动物的解决方案中使用的方法类似的方法来解决。这也意味着一个解决方案不能使用计算机软件包，如GFUN或微分逼近。
英文摘要：
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.
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