与自反的n-color有序分拆相关的一些恒等式

首先,给出了偶数2v的自反的n-color有序分拆与v+1,v-1的n-color有序分拆之间的一个组合双射,并利用相应的计数公式得到了一个组合恒等式.其次,给出了正整数自反的n-color有序分拆数与Fibonacci数、Lucas数之间的一个关系式,并利用此关系式给出了偶数与奇数的自反的n-color有序分拆之间的一个组合双射.最后,给出了一些涉及正整数v的自反的n-color有序分拆数与其它有约束条件的有序分拆数之间的分拆恒等式.

Some Identities Related to the Self-Inverse n-color Compositions

Firstly, we give a combinatorial bijection between the self-inverse n-color compositions of 2ν the n-color compositions of ν+1 along with the n-color compositions of ν-1 in this paper, and we also obtain a combinatorial identity by using some related enumeration formulas. Then, we give a relationship about the number of the self-inverse n-color compositions of positive integer, the Fibonacci number and the Lucas number. In addition, a combinatorial bijection between the self-inverse n-color compositions of odd and the self-inverse n-color compositions of even is presented. Finally, we get some identities about the number of the self-inverse n-color compositions of positive integer and the number of the others compositions with constraint conditions.