Year: 2025
Type: article
Abstract: 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.
DOI: 10.37236/13631
Authors: Aram Bingham, Néstor Fernando Díaz Morera
Institutions: University of Chile, Fitchburg State University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411450183