正整数n的分部量不小于2的有序分拆数  

The number of ordered splits where the components of a positive integer n are not less than 2

作　　者：唐保祥[1] 任韩[2] TANG Baoxiang;REN Han(School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China;Department of Mathematics, East China Normal University, Shanghai 200062, China)

机构地区：[1]天水师范学院数学与统计学院,甘肃天水741001 [2]华东师范大学数学系,上海200062

出　　处：《中山大学学报（自然科学版）》2019年第4期115-118,共4页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11171114)

摘　　要：首先利用递推方法求出了正整数 n 各分部量不大于2的分拆数的公式;其次建立了正整数 n 各分部量不大于2的有序分拆的集合与正整数 n +2各分部量不小于2的有序分拆集合之间的双射,从而得到了正整数 n +2各分部量不小于2的有序分拆数的公式;最后给出了正整数 n 的各分部量不大于3和4的有序分拆数的递推关系式,以及正整数 n 各分部量是2,或3,或4的有序分拆数的递推关系式。Firstly, the formula of the fraction of positive integer n is not more than 2 is obtained by using the recursive method. Secondly, the bijection of the ordered split sets between the fraction of positive integer n is not more than 2 and the fraction of positive integer n +2 is not less than 2 is established, so that the formula for calculating the ordered split number of the positive integer n +2 is not less than 2 is obtained. Finally, when the fraction of positive integer n is not more than 3 or 4, and is 2, 3 or 4, the recursive relations of the ordered split number are given.

关 键 词：有序分拆 递推关系式 双射 

分 类 号：O157[理学—数学]