Skip to Main content Skip to Navigation
Conference papers

On some generalized $q$-Eulerian polynomials

Abstract : The $(q,r)$-Eulerian polynomials are the $(\mathrm{maj-exc, fix, exc})$ enumerative polynomials of permutations. Using Shareshian and Wachs' exponential generating function of these Eulerian polynomials, Chung and Graham proved two symmetrical $q$-Eulerian identities and asked for bijective proofs. We provide such proofs using Foata and Han's three-variable statistic $(\mathrm{inv-lec, pix, lec})$. We also prove a new recurrence formula for the $(q,r)$-Eulerian polynomials and study a $q$-analogue of Chung and Graham's restricted Eulerian polynomials. In particular, we obtain a symmetrical identity for these restricted $q$-Eulerian polynomials with a combinatorial proof.
Document type :
Conference papers
Complete list of metadata

Cited literature [19 references]  Display  Hide  Download

https://hal.inria.fr/hal-01229749
Contributor : Alain Monteil <>
Submitted on : Tuesday, November 17, 2015 - 10:21:02 AM
Last modification on : Wednesday, July 8, 2020 - 12:43:15 PM
Long-term archiving on: : Friday, April 28, 2017 - 7:44:36 PM

File

dmAS0135.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01229749, version 1

Citation

Zhicong Lin. On some generalized $q$-Eulerian polynomials. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.409-420. ⟨hal-01229749⟩

Share

Metrics

Record views

222

Files downloads

219