A short proof of a result of Foata and Zeilberger
Let \(n\) be a positive integer and denote by \(S_n\) the set of all permutations \(\pi\) on the \(n\) symbols \(1,2,\dots, n\). Consider the \(\text{den } \pi\) and \(\text{bis }\pi\) statistics on \(S_n\). In 1990 D. Foata and D. Zeilberger proved the theorem \(\text{den } \pi= \text{den bis }\pi\). In this paper the author provides a straightforward proof of this theorem.
scientific article; zbMATH DE number 820040