Permutation patterns, stanley symmetric functions, and the edelman-greene correspondence

Generalizing the notion of a vexillary permutation, we introduce a filtration of S1 by the number of Edelman-Greene tableaux of a permutation, and show that each filtration level is characterized by avoiding a finite set of patterns. In doing so, we show that if w is a permutation containing v as a pattern, then there is an injection from the set of Edelman-Greene tableaux of v to the set of Edelman-Greene tableaux of w which respects inclusion of shapes. We also consider the set of permutations whose Edelman-Greene tableaux have distinct shapes, and show that it is closed under taking patterns.