文章摘要
郭育红.正整数不含分部量2有序分拆的一些恒等式[J].,2018,58(4):437-440
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
  
DOI:10.7511/dllgxb201804015
中文关键词: 正整数的有序分拆  In-place  恒等式  生成函数  组合双射证明
英文关键词: compositions of positive integer  In-place  identity  generating function  combinatorial bijective proof
基金项目:国家自然科学基金资助项目(11461020).
作者单位
郭育红  
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中文摘要:
      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.
英文摘要:
      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.
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