正整数不含分部量2有序分拆的一些恒等式

Some identities related to compositions of positive integers without 2′s

首先得到了关于正整数n不含分部量2,且分部量1出现In-place偶数次的分拆恒等式,以及偶分部量出现In-place偶数次的分拆恒等式,并给出了组合双射证明.同时将分拆恒等式做了相应的推广.最后还给出了正整数n不含分部量2的有序分拆中,奇分部量有两种形式的分拆数的生成函数及递推关系.

Some identities related to compositions of positive integer n without 2′s such that part 1 appears In-place with even multiplicity,and each even part appears In-place with even multiplicity are obtained.Furthermore,the combinatorial bijective proofs are given,and these identities are generalized as well.In addition,the generating function,recurrence relation are obtained for the compositions of positive integer n without 2′s where each odd part can be of two kinds.