A new cyclic sieving phenomenon for Catalan objects

Abstract

Based on computational experiments, Jim Propp and Vic Reiner suspected that there might exist a sequence of combinatorial objects $X_n$, each carrying a natural action of the cyclic group $C_{n-1}$ of order $n-1$ such that the triple $\left(X_n,C_{n-1},\frac{1}{[n+1{]}_q}{\left[\genfrac{}{}{0ex}{}{2n}{n}\right]}_q\right)$ exhibits the cyclic sieving phenomenon. We prove their suspicion right.

4 pages