The main purpose of this paper is to prove that the Bruhat-Chevalley ordering of the
symmetric group when restricted to the fixed-point-free involutions forms an EL-shellable …

We define combinatorially a partial order on the set partitions and show that it is equivalent
to the Bruhat-Chevalley-Renner order on the upper triangular matrices. By considering …

We exhibit a connection between two statistics on set partitions, the intertwining number and
the depth-index. In particular, results link the intertwining number to the algebraic geometry …

Borel subgroup orbits of the classical symmetric space $ SO_ {2n}/GL_n $ are parametrized
by $ DIII $$(n, n) $-clans. We group the clans into" sects" corresponding to Schubert cells of …

By using the theory of linear algebraic monoids, we introduce a new class of spherical
embeddings of symmetric varieties. Along the way we determine when an antiinvolution on …

We define combinatorially a partial order on the set partitions and show that it is equivalent
to the Bruhat–Chevalley–Renner order on the upper triangular matrices. By considering …

Borel subgroup orbits of the classical symmetric space SO2n/GLn are parametrized by (n, n)-
clans of type DIII. We describe explicit bijections between such clans, diagonally symmetric …

Let G be a reductive group, B be a Borel subgroup, and let K be a symmetric subgroup of G.
The study of B orbits in a symmetric variety G/K or, equivalently, the study of K orbits in a flag …

We study the restriction to the symmetric group, S n \documentclass[12pt]{minimal} \usepackage{amsmath}
\usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} …

arXiv:1703.09881v1 [math.CO] 29 Mar 2017 The genesis of involutions (polarizations and
lattice paths) Page 1 arXiv:1703.09881v1 [math.CO] 29 Mar 2017 The genesis of involutions …