On cyclic Schur-positive sets of permutations

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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 existence 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 either horizontal or vertical rotation are cyclic Schur-positive. The proof unveils a new equidistribution phenomenon of descent sets on permutations, provides affirmative solutions to conjectures by the last two authors and by Adin-Gessel-Reiner-Roichman, and yields new examples of Schur-positive sets.
TitleOn cyclic Schur-positive sets of permutations
CreatorElizalde, S.
Bloom, Jonathan
Roichman, Y.
PublisherElectronic Journal of Combinatorics
Academic DepartmentMathematics
DivisionNatural Sciences
OrganizationLafayette College
Date IssuedApril 17, 2020
Date Available2020-04-30
TypeArticle
LanguageEnglish
Bibliographic CitationBloom, J., S. Elizalde and Y. Roichman (2020 Apr 17) "On cyclic Schur-positive sets of permutations." Electronic Journal of Combinatorics 27 (2): P2.6.
Standard IdentifierDOI 10.37236/8974
Handle 10385/1544bp59w
Permalinkhttp://hdl.handle.net/10385/1544bp59w
Rights Statement Creative Commons - Attribution, No Derivatives Creative Commons - Attribution, No Derivatives
Rights HoldersElizalde, S.
Bloom, Jonathan
Roichman, Y.
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