不含L连续数组的排列计数问题的研究

A Study on the Enumeration Problems of the Arrangements Excluding L-consecutive Arrays

[1]中定义了不含连续数对的排列并用容斥原理给出了它的计数公式.本文由此问题出发定义了由1,2,3,…,n作成的不含L(L≥3)连续数组的全排列,引入算子(·,·),通过运算(·,·)可以由不含连续数对的排列构造得到不含L(L≥3)连续数组的排列,综合利用乘法原则、加法原则和数学归纳法求得了由1,2,3,…,n作成的不含L连续数组的全排列的计数公式.

The arrangement excluding successive arrays is presented in [ 1 ]. And its enumerating formular is obtained by using Inclusion-Exclusion Principle. In this paper, the arrangements which do not contain L- consecutive （L≥3） arrays are defined. Firstly, an operator О（.,.） is introduced. Then an arrangment not containing L -consecutive arrays can be obtained from an arrangement excluding successive arrays by this operator. Lastly, by using the multiplication principle, addition principle and combining the principle of mathematical induction, the enumerating formulars for the arrangments not excluding L -consecutive arrays are obtained.