A new bijection relating q-Eulerian polynomials

On the set of permutations of a finite set, we construct a bijection which maps the 3-vector of statistics (maj−exc,des,exc)(maj−exc,des,exc) to a 3-vector (maj2,des2˜,inv2) associated with the q-Eulerian polynomials introduced by Shareshian and Wachs (2014) [10].