A New Encoding of Permutations by Laguerre Histories

  • Sherry H.F. Yan
  • Hao Zhou
  • Zhicong Lin
DOI: https://doi.org/10.37236/8661

Abstract

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.

Published
2019-09-13
Issue
Volume 26, Issue 3 (2019)
Article Number
P3.47