On cyclic schur-positive sets of permutations

Jonathan Bloom, Sergi Elizalde, Yuval Roichman

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3 Scopus citations

Abstract

We introduce a notion of cyclic Schur-positivity for sets of permutations, which naturally extends the classical notion of Schur-positivity, and it involves the exis- tence of a bijection from permutations to standard Young tableaux that preserves the cyclic descent set. Cyclic Schur-positive sets of permutations are always Schur- positive, but the converse does not hold, as exemplified by inverse descent classes, Knuth classes and conjugacy classes. In this paper we show that certain classes of permutations invariant under ei- ther horizontal or vertical rotation are cyclic Schur-positive. The proof unveils a new equidistribution phenomenon of descent sets on permutations, provides affr- mative solutions to conjectures by the last two authors and by Adin{Gessel{Reiner{ Roichman, and yields new examples of Schur-positive sets.

Original languageEnglish
Article numberP2.6
JournalElectronic Journal of Combinatorics
Volume27
Issue number2
DOIs
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© The authors. Released under the CC BY-ND license (International 4.0).

Funding

Partially supported by a Bar-Ilan University visiting grant. Partially supported by Simons Foundation grant #280575. Partially supported by an MIT-Israel MISTI grant and by the Israel Science Foundation, grant no. 1970/18. ∗Partially supported by a Bar-Ilan University visiting grant. †Partially supported by Simons Foundation grant #280575. Corresponding author. ‡Partially supported by an MIT-Israel MISTI grant and by the Israel Science Foundation, grant no.

FundersFunder number
Simons Foundation280575
Bar-Ilan University
Israel Science Foundation1970/18

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