简单立方格上三维有向动物的组合数学
Combinatorics of 3D directed animals on a simple cubic lattice
摘要：
我们提供组合参数的基础上的一个二维扩展的局部自由半群，使我们能够计算的增长率，$Λ$，的配分函数$Z_N=N^θΛ^N$的$N$ -粒子定向动物（$N\gg 1$）在一个简单的立方晶格在三维空间。通过建立格动物的特殊构形与2D射影局部自由半群中的一类词的等价之间的双射，我们发现用$Λ= 2(\sqrt{2}+1) \approx 4.8284$找到了$\ln Λ= \lim_{N\to\infty} \ln Z_N / N$.
英文摘要：
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 $Λ= 2(\sqrt{2}+1) \approx 4.8284$.
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。
