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• W2009658434 abstract "We introduce two partially ordered sets, P n A and P n B , of the same cardinalities as the type-A and type-B noncrossing partition lattices. The ground sets of P n A and P n B are subsets of the symmetric and the hyperoctahedral groups, consisting of permutations which avoid certain patterns. The order relation is given by (strict) containment of the descent sets. In each case, by means of an explicit order-preserving bijection, we show that the poset of restricted permutations is an extension of the refinement order on noncrossing partitions. Several structural properties of these permutation posets follow, including self-duality and the strong Sperner property. We also discuss posets Q n A and Q n B similarly associated with noncrossing partitions, defined by means of the excedance sets of suitable pattern-avoiding subsets of the symmetric and hyperoctahedral groups." @default.
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• W2009658434 date "2000-06-01" @default.
• W2009658434 modified "2023-09-26" @default.
• W2009658434 title "A self-dual poset on objects counted by the Catalan numbers and a type-B analogue" @default.
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• W2009658434 doi "https://doi.org/10.1016/s0012-365x(99)00397-0" @default.
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