RSK Tableaux and the Weak Order on Fully Commutative Permutations
RSK Tableaux and the Weak Order on Fully Commutative Permutations
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 …