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Generalizing the notion of a vexillary permutation, we introduce a filtration of S∞ 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… (More)

My research has focused on the representation theory of the symmetric group and related parts of symmetric function theory and Schubert calculus. I'm also interested in permutation combi-natorics, particularly pattern avoidance and the theory of reduced words. Cohomology classes of rank varieties and a conjecture of Liu, preprint arXiv:1410.7419. 2015… (More)

The study of permutations is of central importance to mathematics. Computation with permutation groups has typically been limited to systems such as GAP and Magma. In this paper we describe cl-permutation, a system for doing computations with permutation groups in ANSI Common Lisp. Homomesies, a recent concept introduced by Propp and Roby, are elaborated… (More)

a r t i c l e i n f o a b s t r a c t 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… (More)

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