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https://hdl.handle.net/10316/11176
Title: | A bijection between noncrossing and nonnesting partitions of types A, B and C | Authors: | Mamede, Ricardo | Keywords: | Root systems; Noncrossing partitions; Nonnesting partitions; Bijection | Issue Date: | 2009 | Publisher: | Centro de Matemática da Universidade de Coimbra | Citation: | Pré-Publicações DMUC. 09-12 (2009) | Abstract: | The total number of noncrossing partitions of type is the nth Catalan number 1 n+1 2n n when = An−1, and the coefficient binomial 2n n when = Bn or Cn, and these numbers coincide with the correspondent number of nonnesting partitions. For type A, there are several bijective proofs of this equality; in particular, the intuitive map, which locally converts each crossing to a nesting, is one of them. In this paper we present a bijection between nonnesting and noncrossing partitions of types A,B and C that generalizes the type A bijection that locally converts each crossing to a nesting. | URI: | https://hdl.handle.net/10316/11176 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Vários |
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A bijection between noncrossing and nonnesting partitions.pdf | 207.85 kB | Adobe PDF | View/Open |
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