A bijection between noncrossing and nonnesting partitions of types A and B
نویسنده
چکیده
The total number of noncrossing partitions of type Ψ is the nth Catalan number 1 n+1 (
منابع مشابه
A bijection between noncrossing and nonnesting partitions of types A, B and C
The total number of noncrossing partitions of type Ψ is equal to the nth Catalan number 1 n+1 ( 2n n ) when Ψ = An−1, and to the corresponding binomial coefficient ( 2n n ) when Ψ = Bn or Cn. These numbers coincide with the corresponding number of nonnesting partitions. For type A, there are several bijective proofs of this equality; in particular, the intuitive map, which locally converts each...
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We present type preserving bijections between noncrossing and nonnesting partitions for all classical reflection groups, answering a question of Athanasiadis and Reiner. The bijections for the abstract Coxeter types B, C and D are new in the literature. To find them we define, for every type, sets of statistics that are in bijection with noncrossing and nonnesting partitions, and this correspon...
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We present an elementary type preserving bijection between noncrossing and nonnesting partitions for all classical reflection groups, answering a question of Athanasiadis.
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We present an explicit bijection between noncrossing and nonnesting partitions of Coxeter systems of type D which preserves openers, closers and transients. 1. Overview The lattice of set partitions of a set of n elements can be interpreted as the intersection lattice for the hyperplane arragement corresponding to a root system of type An−1, i.e. the symmetric group of n objects, Sn. In particu...
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The number of noncrossing partitions of {1, 2, . . . , n} with fixed block sizes has a simple closed form, given by Kreweras, and coincides with the corresponding number for nonnesting partitions. We show that a similar statement is true for the analogues of such partitions for root systems B and C, defined recently by Reiner in the noncrossing case and Postnikov in the nonnesting case. Some of...
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