https://hal.inria.fr/hal-01229676Albert, MichaelMichaelAlbertDepartment of Computer Science, University of Otago - University of Otago [Dunedin, Nouvelle-Zélande]Bouvel, MathildeMathildeBouvelLaBRI - Laboratoire Bordelais de Recherche en Informatique - UB - Université de Bordeaux - École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB) - CNRS - Centre National de la Recherche ScientifiqueOperators of equivalent sorting power and related Wilf-equivalencesHAL CCSD2013permutationstacksortingenumerationWilf-equivalence[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]Monteil, AlainAlain Goupil and Gilles Schaeffer2015-11-17 10:19:452022-06-25 10:35:592015-11-17 10:25:02enConference papershttps://hal.inria.fr/hal-01229676/document10.46298/dmtcs.2333application/pdf1We 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.