A new bijection relating $q$-Eulerian polynomials

Ange Bigeni (1)

1 CTN - Combinatoire, théorie des nombres

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).}

Mots clés: q-Eulerian polynomials; descents; ascents; major index; exceedances; inversions

Domaines: Combinatoire [math.CO]

Ange Bigeni. A new bijection relating $q$-Eulerian polynomials. 2015. ⟨hal-01166524v2⟩