Enumerating Up-Side Self-Avoiding Walks on Integer Lattices
Enumerating Up-Side Self-Avoiding Walks on Integer Lattices
复制标题
枚举整数格上的上侧自回避游走
DOI：
10.37236/1255
复制
发表时间：
1996
影响因子：
0.7
通讯作者：
L. Williams
中科院分区：
文献类型：
--
作者：
L. Williams
自我回避行走（saw）是在晶格上不经过同一点两次的路径。尽管数学家们已经研究了50多年的锯，但n步锯的数量是未知的。本文研究了这一问题的一个特殊情况，找到了n阶“上侧”锯（ussaws）的数目，这些锯只能向上和向侧面移动。给出了用分解和递归方法生成函数在各种格上求n步乌索数的公式。
A self-avoiding walk (saw) is a path on a lattice that does not pass through the same point twice. Though mathematicians have studied saws for over flfty years, the number of n-step saws is unknown. This paper examines a special case of this problem, flnding the number of nstep \up-side" saws (ussaws), saws restricted to moving up and sideways. It presents formulas for the number of n-step ussaws on various lattices, found using generating functions with decomposition and recursive methods.