  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.

Combinatorics