Author(s):
Mamede, Ricardo 
Date: 2009
Persistent ID: http://hdl.handle.net/10316/11176
Origin: Estudo Geral - Universidade de Coimbra
Subject(s): Root systems; Noncrossing partitions; Nonnesting partitions; Bijection
Document details
A bijection between noncrossing and nonnesting partitions of types A, B and C
Description
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
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
Document Type
Preprint
Language English
Language English
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