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 language | English |
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Article number | P2.6 |
Journal | Electronic Journal of Combinatorics |
Volume | 27 |
Issue number | 2 |
DOIs | |
State | Published - 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.
Funders | Funder number |
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Simons Foundation | 280575 |
Bar-Ilan University | |
Israel Science Foundation | 1970/18 |