A Summation Formula Related to \(q\)-Eulerian Polynomials

Abstract

Brenti (J. Combin. Theory Ser. A \(91 (2000))\) considered a \(q\)-analogue of the Eulerian polynomials by enumerating permutations in the symmetric group \(S_n\) with respect to the numbers of excedances and cycles. Here we establish a connection between these \(q\)-Eulerian polynomials and some infinite generating functions.