A bijection between certain non-crossing partitions and sequences

Abstract

We present a bijection between non-crossing partitions of the set $[2n+1]$ into $n+1$ blocks such that no block contains two consecutive integers, and the set of sequences $\{s_i{\}}_1^n$ such that $1\le s_i\le i$, and if $s_i=j$, then $s_{i-r}\le j-r$ for $1\le r\le j-1$.

8 pages, 6 figures