Skip to Main content Skip to Navigation
Conference papers

Operators of equivalent sorting power and related Wilf-equivalences

Abstract : We study sorting operators $\textrm{A}$ on permutations that are obtained composing Knuth's stack sorting operator \textrmS and the reverse operator $\textrm{R}$, as many times as desired. For any such operator $\textrm{A}$, we provide a bijection between the set of permutations sorted by $\textrm{S} \circ \textrm{A}$ and the set of those sorted by $\textrm{S} \circ \textrm{R} \circ \textrm{A}$, proving that these sets are enumerated by the same sequence, but also that many classical permutation statistics are equidistributed across these two sets. The description of this family of bijections is based on an apparently novel bijection between the set of permutations avoiding the pattern $231$ and the set of those avoiding $132$ which preserves many permutation statistics. We also present other properties of this bijection, in particular for finding families of Wilf-equivalent permutation classes.
Document type :
Conference papers
Complete list of metadata

Cited literature [12 references]  Display  Hide  Download
Contributor : Alain Monteil <>
Submitted on : Tuesday, November 17, 2015 - 10:19:45 AM
Last modification on : Friday, November 13, 2020 - 9:42:02 AM
Long-term archiving on: : Thursday, February 18, 2016 - 11:36:05 AM


Publisher files allowed on an open archive


  • HAL Id : hal-01229676, version 1



Michael Albert, Mathilde Bouvel. Operators of equivalent sorting power and related Wilf-equivalences. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.671-682. ⟨hal-01229676⟩



Record views


Files downloads