关于正整数不含分部量2的有序分拆的几个组合双射

Several combinatorial bijections about compositions without 2's of positive integers

利用正整数有序分拆的共轭分拆,分别给出了偶数2k、奇数2k+1和正整数n的不含分部量2的自反的有序分拆数的递推关系式的组合双射证明.此外,还给出了NAGI关于正整数n不含分部量2的有序分拆数的一个恒等式的不同组合双射.

Using the conjugate of compositions,we present combinatorial bijective proofs of the recurrence relation of the self-inverse compositions without 2's of even 2k,2's of odd 2k+1,and without 2's of positive integer n,respectively.In addition,we also obtain the combinatorial bijection of an identity which was obtained by MUNAGI relating to the number of the compositions without 2's of positive integer n.The methods used in this paper are different from the proofs of MUNAGI.