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For each fully commutative permutation, we construct a "boolean core," whichis the maximal boolean permutation in its principal order ideal under the rightweak order. We partition the set of fully commutative permutations into therecently defined crowded and uncrowded elements, distinguished by whether ornot their RSK insertion tableaux satisfy a sparsity condition. We show that afully commutative element is uncrowded exactly when it shares the RSK insertiontableau with its boolean core. We present the dynamics of the right weak orderon fully commutative permutations, with particular interest in when they changefrom uncrowded to crowded. In particular, we use consecutive permutationpatterns and descents to characterize the minimal crowded elements under theright weak order.

RSK tableaux and the weak order on fully commutative permutations