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浙江大学学报（理学版）
Journal of Zhejiang University (Science Edition)  2023, Vol. 50 Issue (3): 261-265    DOI: 10.3785/j.issn.1008-9497.2023.03.001
Mathematics and Computer Science     
Several identities and combinatorial proofs for compositions related to the part of size 1
Yuhong GUO()
School of Mathematics and Statistics，Hexi University，Zhangye 734000，Gansu Province，China
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Abstract  

The compositions with part of size 1 at the left or the right of positive integers are studied, and the relation between these compositions and the Fibonacci numbers is obtained. And then using the well-known composition identities related to Fibonacci numbers, several new identities are obtained, The combinational bijective proofs are provided.

Key words： compositions      part of size 1      Fibonacci numbers      identity      combinatorial proof     
Received: 13 December 2021      Published: 19 May 2023
CLC:  O 157  
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Yuhong GUO
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Yuhong GUO. Several identities and combinatorial proofs for compositions related to the part of size 1. Journal of Zhejiang University (Science Edition), 2023, 50(3): 261-265.

URL:

https://www.zjujournals.com/sci/EN/Y2023/V50/I3/261


与有序分拆的分部量1相关的恒等式及组合证明

研究了正整数的分部量1在首、末两端的有序分拆，给出了此类有序分拆数与Fibonacci数之间的关系式。利用熟知的与Fibonacci数相关的有序分拆恒等式，得到几个新的分拆恒等式，并给出了组合双射证明。


关键词： 有序分拆,  分部量1,  Fibonacci 数,  恒等式,  组合证明 
Fig.1 Zig-Zag graph of compositions for 14
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