  For each fully commutative permutation, we construct a "boolean core," which
is the maximal boolean permutation in its principal order ideal under the right
weak order. We partition the set of fully commutative permutations into the
recently defined crowded and uncrowded elements, distinguished by whether or
not their RSK insertion tableaux satisfy a sparsity condition. We show that a
fully commutative element is uncrowded exactly when it shares the RSK insertion
tableau with its boolean core. We present the dynamics of the right weak order
on fully commutative permutations, with particular interest in when they change
from uncrowded to crowded. In particular, we use consecutive permutation
patterns and descents to characterize the minimal crowded elements under the
right weak order.

Combinatorics