In this paper, we show that the Bruhat order on any sect of a symmetric variety of type $AIII$ is lexicographically shellable. Our proof proceeds from a description of these posets as rook placements in a partition shape which fits in a $p \times q$ rectangle. This allows us to extend an EL-labeling of the rook monoid given by Can to an arbitrary sect. As a special case, our result implies that the Bruhat order on matrix Schubert varieties is lexicographically shellable.
@article{10_37236_13631,
author = {Aram Bingham and N\'estor Fernando D{\'\i}az Morera},
title = {Lexicographic shellability of sects},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {2},
doi = {10.37236/13631},
zbl = {8062184},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13631/}
}
TY - JOUR
AU - Aram Bingham
AU - Néstor Fernando Díaz Morera
TI - Lexicographic shellability of sects
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/13631/
DO - 10.37236/13631
ID - 10_37236_13631
ER -
%0 Journal Article
%A Aram Bingham
%A Néstor Fernando Díaz Morera
%T Lexicographic shellability of sects
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/13631/
%R 10.37236/13631
%F 10_37236_13631
Aram Bingham; Néstor Fernando Díaz Morera. Lexicographic shellability of sects. The electronic journal of combinatorics, Tome 32 (2025) no. 2. doi: 10.37236/13631
