Permutation patterns, Stanley symmetric functions, and generalized Specht modules

@article{Billey2014PermutationPS,
  title={Permutation patterns, Stanley symmetric functions, and generalized Specht modules},
  author={Sara C. Billey and Brendan Pawlowski},
  journal={J. Comb. Theory, Ser. A},
  year={2014},
  volume={127},
  pages={85-120}
}
Abstract Generalizing the notion of a vexillary permutation, we introduce a filtration of S ∞ by the number of terms in the Stanley symmetric function, with the kth filtration level called the k-vexillary permutations. We show that for each k, the k-vexillary permutations are characterized by avoiding a finite set of patterns. A key step is the construction of a Specht series, in the sense of James and Peel, for the Specht module associated with the diagram of a permutation. As a corollary, we… 
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