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.
@article{10_37236_8974,
author = {Jonathan Bloom and Sergi Elizalde and Yuval Roichman},
title = {On cyclic {Schur-positive} sets of permutations},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {2},
doi = {10.37236/8974},
zbl = {1439.05222},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8974/}
}
TY - JOUR
AU - Jonathan Bloom
AU - Sergi Elizalde
AU - Yuval Roichman
TI - On cyclic Schur-positive sets of permutations
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/8974/
DO - 10.37236/8974
ID - 10_37236_8974
ER -
%0 Journal Article
%A Jonathan Bloom
%A Sergi Elizalde
%A Yuval Roichman
%T On cyclic Schur-positive sets of permutations
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/8974/
%R 10.37236/8974
%F 10_37236_8974
Jonathan Bloom; Sergi Elizalde; Yuval Roichman. On cyclic Schur-positive sets of permutations. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/8974
