论文标题
在简单的立方晶格上的3D定向动物的组合学
Combinatorics of 3D directed animals on a simple cubic lattice
论文作者
论文摘要
我们根据本地无网群的二维扩展提供组合论点，使我们能够计算分区功能的$λ$的增长率$ z_n = n^θλ^n $ $ n $ n $ particle的指向动物（$ n \ gg 1 $）的增长率（$ n $ n $ n $ n $ n^θλ^n $）在简单的立方体lattice lattice lattice lattice lattice lattice lattice lattice lattice specs中的三二维和三二维镜。建立晶格动物的特定配置与2D投影本地的无本地半群中的一类单词之间的两者之间的两者，我们发现我们发现$ \lnλ= \ lim_ {n \ to \ infty} \ ln} \ ln z_n / n $，带有$λ= 2（\ sqrt = 2（\ sqrt {2}+1}+1）。
We provide combinatorial arguments based on a two-dimensional extension of a locally-free semigroup allowing us to compute the growth rate, $Λ$, of the partition function $Z_N=N^θΛ^N$ of the $N$-particle directed animals ($N\gg 1$) on a simple cubic lattice in a three-dimensional space. Establishing the bijection between the particular configuration of the lattice animal and a class of equivalences of words in the 2D projective locally-free semigroup, we find we find $\ln Λ= \lim_{N\to\infty} \ln Z_N / N$ with $Λ= 2(\sqrt{2}+1) \approx 4.8284$.
