| 郭育红.关于反共轭有序分拆的几个恒等式[J].数学研究及应用,2018,38(5):441~448 |
| 关于反共轭有序分拆的几个恒等式 |
| Several Identities for Inverse-Conjugate Compositions |
| 投稿时间：2017-10-27 修订日期：2018-05-17 |
| DOI：10.3770/j.issn:2095-2651.2018.05.001 |
| 中文关键词: 反共轭有序分拆 恒等式 Fibonacci数 Tribonacci数 双射证明 |
| 英文关键词:inverse-conjugate compositions identity Fibonacci number Tribonacci number bijective proof |
| 基金项目:国家自然科学基金资助项目(Grant No.11461020). |
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| 中文摘要: |
| 本文给出了与正整数的分部量不超过$3$的反共轭有序分拆、分部量是$1, 2$的有序分拆、分部量是奇数的有序分拆、分部量是大于$1$的有序分拆相关的几个分拆恒等式. 此外，还给出了正整数的分部量不超过$k$的反共轭有序分拆的一个关系式的组合双射证明. |
| 英文摘要: |
| In this paper, we first present several identities related to the inverse-conjugate compositions having parts of size $\leq 3$, the compositions into parts equal to $1$ or $2$, the compositions into odd parts and the compositions into parts greater than $1$. In addition, we provide a bijective proof of a relation for inverse-conjugate compositions having parts of size $\leq k$. |
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