On rotated Schur-positive sets

Sergi Elizalde, Yuval Roichman

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

The problem of finding Schur-positive sets of permutations, originally posed by Gessel and Reutenauer, has seen some recent developments. Schur-positive sets of pattern-avoiding permutations have been found by Sagan et al. and a general construction based on geometric operations on grid classes has been given by the authors. In this paper we prove that horizontal rotations of Schur-positive subsets of permutations are always Schur-positive. The proof applies a cyclic action on standard Young tableaux of certain skew shapes and a jeu-de-taquin type straightening algorithm. As a consequence of the proof we obtain a notion of cyclic descent set on these tableaux, which is rotated by the cyclic action on them.

Original languageEnglish
Pages (from-to)121-137
Number of pages17
JournalJournal of Combinatorial Theory - Series A
Volume152
DOIs
StatePublished - Nov 2017

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Inc.

Keywords

  • Cyclic action
  • Cyclic descent
  • Horizontal rotation
  • Schur-positivity
  • Standard Young tableau

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