2019/03/18 by Aram Bingham, Bingham, Aram, Ozlem Ugurlu +1
Mathematics · #05A15 #14M15 #14M17 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15 #msc:14M15 #msc:14M17
paper · pdf · doi:10.48550/arxiv.1903.07229
arxiv created 2020/01/20 · arxiv updated 2020/01/22
We examine Borel subgroup orbits in the classical symmetric space of type CI, which are parametrized by skew symmetric (n, n)-clans. We describe bijections between such clans, certain weighted lattice paths, and pattern-avoiding signed involutions, and we give a cell decomposition of the symmetric space in terms of collections of clans called sects. The largest sect with a conjectural closure order is isomorphic (as a poset) to the Bruhat order on partial involutions.