Stirling Permutations, Cycle Structure of Permutations and Perfect Matchings

Abstract

In this paper we provide constructive proofs that the following three statistics are equidistributed: the number of ascent plateaus of Stirling permutations of order $n$, a weighted variant of the number of excedances in permutations of length $n$ and the number of blocks with even maximal elements in perfect matchings of the set $\{1,2,3,\ldots,2n\}$.