| Several Identities for Inverse-Conjugate Compositions |
| Received:October 27, 2017 Revised:May 17, 2018 |
| Key Words:
inverse-conjugate compositions identity Fibonacci number Tribonacci number bijective proof
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11461020). |
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| Abstract: |
| 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 $\leq k$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2018.05.001 |
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