A Consecutive Lehmer Code for Parabolic Quotients of the Symmetric Group.

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

Abstract

In this article we define an encoding for parabolic permutations that distin-guishes between parabolic 231-avoiding permutations. We prove that the compo-nentwise order on these codes realizes the parabolic Tamari lattice, and conclude a direct and simple proof that the parabolic Tamari lattice is isomorphic to a certain ν-Tamari lattice, with an explicit bijection. Furthermore, we prove that this bijec-tion is closely related to the map Θ used when the lattice isomorphism was first proved in (Ceballos, Fang and Mühle, 2020), settling an open problem therein.

Details

Original languageEnglish
Article numberP3.53
Number of pages28
JournalThe Electronic journal of combinatorics
Volume28
Issue number3
Publication statusPublished - 2021
Peer-reviewedYes

External IDs

Scopus 85115667330

Keywords

Library keywords