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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):
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