Several Identities for Inverse-Conjugate Compositions
Received:October 27, 2017  Revised:May 17, 2018
Key Word: inverse-conjugate compositions   identity   Fibonacci number   Tribonacci number   bijective proof
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11461020).
 Author Name Affiliation Yuhong GUO School of Mathematics and Statistics, Hexi University, Gansu 734000, P. R. China
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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 $\leq k$.