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Abstract: The total number of noncrossing partitions of type $\Psi$ is the $n$thCatalan number $\frac{1}{n+1}\binom{2n}{n}$ when $\Psi=A {n-1}$, and thebinomial $\binom{2n}{n}$ when $\Psi=B n$, and these numbers coincide with thecorrespondent number of nonnesting partitions. For type A, there are severalbijective proofs of this equality, being the intuitive map that locallyconverts each crossing to a nesting one of them. In this paper we present abijection between nonnesting and noncrossing partitions of types A and B thatgeneralizes the type A bijection that locally converts each crossing to anesting.



Autor: Ricardo Mamede

Fuente: https://arxiv.org/







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