A New Encoding of Permutations by Laguerre Histories
A New Encoding of Permutations by Laguerre Histories
We construct a bijection from permutations to some weighted Motzkin paths known as Laguerre histories. As one application of our bijection, a neat $q$-$\gamma$-positivity expansion of the $(\mathrm{inv},\mathrm{exc})$-$q$-Eulerian polynomials is obtained.