  We study the combinatorial properties of vexillary signed permutations, which
are signed analogues of the vexillary permutations first considered by Lascoux
and Sch\"utzenberger. We give several equivalent characterizations of vexillary
signed permutations, including descriptions in terms of essential sets and
pattern avoidance, and we relate them to the vexillary elements introduced by
Billey and Lam.
