  We define and construct the "canonical reduced word" of a boolean
permutation, and show that the RSK tableaux for that permutation can be read
off directly from this reduced word. We also describe those tableaux that can
correspond to boolean permutations, and enumerate them. In addition, we
generalize a result of Mazorchuk and Tenner, showing that the "run" statistic
influences the shape of the RSK tableau of arbitrary permutations, not just of
those that are boolean.
