  Motivated by recent work with Mazorchuk, we characterize the conditions under
which the intersection of two principal order ideals in the Bruhat order is
boolean. That characterization is presented in three versions: in terms of
reduced words, in terms of permutation patterns, and in terms of permutation
support. The equivalence of these properties follows from an analysis of what
it means to have a specific letter repeated in a permutation's reduced words;
namely, that a specific 321-pattern appears.
