二维格点上有向动物的平均位周长
Average site perimeter of directed animals on the two-dimensional lattices
摘要：
我们引入新的组合（双射）方法，使我们能够计算一个给定的区域，包括网站周长的定向动物的三个参数的平均值。我们的结果涵盖了正方形格上的任何单线源的有向动物及其有界变体，并且我们给出了三角形格上的对应结果。因此，我们证明了Conway和Le Borgne的猜想。所使用的技术是基于Viennot的对应关系之间的有向动物和堆件（或元素的部分交换幺半群）。
英文摘要：
We introduce new combinatorial (bijective) methods that enable us to compute the average value of three parameters of directed animals of a given area, including the site perimeter. Our results cover directed animals of any one-line source on the square lattice and its bounded variants, and we give counterparts for most of them in the triangular lattices. We thus prove conjectures by Conway and Le Borgne. The techniques used are based on Viennot's correspondence between directed animals and heaps of pieces (or elements of a partially commutative monoid).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
