A bijection between noncrossing and nonnesting partitions of types A, B and C
The total number of noncrossing partitions of type Y is the nth Catalan number 1/(n+1)C(2n,n) when Y=An-1, and the coefficient binomial C(2n,n) when Y=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 partition of types A,B and C that generalizes the type A bijection that locally converts each crossing to a nesting.
Pré-publicações do Departamento de Matemática da Universidade de Coimbra