不相邻重排列的一种计数方法

A Counting Method for Non-Neighboring Rearrangement

当前已经解决了重排列的计数问题,也解决了不相邻排列的计数问题(单排列时),但是当把这两种情况结合起来时,情况就要复杂得多,它实际上是一类很常见的排列问题.该文介绍了这样一类特殊排列———重排列在限制某两种元素不相邻时的一种计数方法,通过将问题进行简化,巧妙处理,得出了这类计数的计算公式.

Counting problems of rearrangement have been solved, so have those of non-neighboring (arrangement) (non-rearrangement). However, the situation becomes much more complicated when the two problems are combined. Nonetheless, this is in fact a quite common arrangement problem. This paper presents a counting method for special rearrangement in which there are two kinds of elements that are restricted to be non-neighboring. A numerical formula is derived by simplification of the (problem) and with a special treatment.