A new descent set statistic on involutions, defined geometrically via their interpretation as matchings, is introduced in this paper, and shown to be equidistributed with the standard one. This concept is then applied to construct explicit cyclic descent extensions on involutions, standard Young tableaux and Motzkin paths. Schur-positivity of the associated quasisymmetric functions follows.
@article{10_37236_11761,
author = {Ron M Adin and Yuval Roichman},
title = {Cyclic descents, matchings and {Schur-positivity}},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {2},
doi = {10.37236/11761},
zbl = {1517.05179},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11761/}
}
TY - JOUR
AU - Ron M Adin
AU - Yuval Roichman
TI - Cyclic descents, matchings and Schur-positivity
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/11761/
DO - 10.37236/11761
ID - 10_37236_11761
ER -
%0 Journal Article
%A Ron M Adin
%A Yuval Roichman
%T Cyclic descents, matchings and Schur-positivity
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/11761/
%R 10.37236/11761
%F 10_37236_11761
Ron M Adin; Yuval Roichman. Cyclic descents, matchings and Schur-positivity. The electronic journal of combinatorics, Tome 30 (2023) no. 2. doi: 10.37236/11761
