A bijection between noncrossing and nonnesting partitions of types A and B
 
 
Description:  The total number of noncrossing partitions of type $\Psi$ is the $n$th Catalan number $\frac{1}{n+1}\binom{2n}{n}$ when $\Psi=A_{n-1}$, and the binomial $\binom{2n}{n}$ when $\Psi=B_n$, 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 talk we present a bijection between nonnesting and noncrossing partitions of types A and B that generalizes the type A bijection that locally converts each crossing to a nesting.
Area(s):
Date:  2009-02-10
Start Time:   15:30
Speaker:  Ricardo Mamede (CMUC/Mat. FCTUC)
Place:  5.5
Research Groups: -Algebra and Combinatorics
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