  On the set of permutations of a finite set, we construct a bijection which
maps the 3-vector of statistics $(maj-exc,des,exc)$ to a 3-vector
$(maj\_2,\widetilde{des\_2},inv\_2)$ associated with the $q$-Eulerian
polynomials introduced by Shareshian and Wachs in \textit{Chromatic
quasisymmetric functions, arXiv:1405.4269(2014).}
