A bijection between noncrossing and nonnesting partitions of types A, B and C

• Autor(es): Mamede, Ricardo
• Data: 2009
• Identificador Persistente: http://hdl.handle.net/10316/11176
• Origem: Estudo Geral - Universidade de Coimbra
• Assunto(s): Root systems; Noncrossing partitions; Nonnesting partitions; Bijection
• Tipo de Documento: Preprint
• Idioma: Inglês

Descrição

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. Centro de Matemática da Universidade de Coimbra