Some Equidistributed Statistics on Genocchi Permutations

Abstract

A Genocchi permutation $\sigma $ of $[2n]$ is a permutation such that $\sigma (2i-1)>2i-1,\quad \sigma (2i)\leq 2i$ for all $i\in \{1, 2, \ldots, 2n\}$. The purpose of this paper is to investigate the equidistribution of several bivariate statistics on the Genocchi permutations.