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- W3014127916 abstract "Given a set of permutations Π, let 𝔖 n (Π) denote the set of permutations in the symmetric group 𝔖 n that avoid every element of Π in the sense of pattern avoidance. Given a subset S of {1,⋯,n-1}, let F S be the fundamental quasisymmetric function indexed by S. Our object of study is the generating function Q n (Π)=∑F Desσ where the sum is over all σ∈𝔖 n (Π) and Desσ is the descent set of σ. We characterize those Π⊆𝔖 3 such that Q n (Π) is symmetric or Schur nonnegative for all n. In the process, we show how each of the resulting Π can be obtained from a theorem or conjecture involving more general sets of patterns. In particular, we prove results concerning symmetries, shuffles, and Knuth classes, as well as pointing out a relationship with the arc permutations of Elizalde and Roichman. Various conjectures and questions are mentioned throughout." @default.
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- W3014127916 date "2020-01-01" @default.
- W3014127916 modified "2023-10-17" @default.
- W3014127916 title "Pattern avoidance and quasisymmetric functions" @default.
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- W3014127916 doi "https://doi.org/10.5802/alco.96" @default.
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