  Clans are combinatorial objects indexing the orbits of $GL(\mathbb{C}^p)
\times GL(\mathbb{C}^q)$ on the variety of flags in $\mathbb{C}^{p+q}$. This
geometry leads to a partial order on the set of clans analogous to weak Bruhat
order on the symmetric group, and we study the saturated chains in this order.
We prove an analogue of the Matsumoto-Tits theorem on reduced words in a
Coxeter group. We also obtain enumerations of reduced word sets for particular
clans in terms of standard tableaux and shifted standard tableaux.
