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

作　　者：郭育红 GUO Yuhong(School of Mathematics and Statistics,Hexi Universit)

机构地区：[1]河西学院数学与统计学院,甘肃张掖734000

出　　处：《大连理工大学学报》2018年第4期437-440,共4页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(11461020)

摘　　要：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.

关 键 词：正整数的有序分拆 In-place 恒等式 生成函数 组合双射证明 

分 类 号：O157[理学—数学]