  We give a necessary and sufficient condition in terms of pattern avoidance
for the conjugates of the bottom vertex in the Bruhat graph attached to an O_n
orbit O in the flag variety for GL_n to have degree equal to the rank of this
graph as a poset, showing that this condition is equivalent to the rational
smoothness of the closure of O. We also give a necessary and sufficient
condition in terms of pattern avoidance for the closure of O to be smooth.
