Algebra and Combinatorics

 

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Author(s)
Ricardo Mamede;

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

Abstract
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.

Preprint series
Pré-publicações do Departamento de Matemática da Universidade de Coimbra

Issue
09-12

Year
2009

 
     
 

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