2023/12/22 by Aram Bingham, Bingham, Aram, Néstor Díaz Morera +1
Mathematics · #05E14 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2312.15093
openalex publication_date 2023/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 × 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.