# A bijection between noncrossing and nonnesting partitions of types A and B - Mathematics > Combinatorics

A bijection between noncrossing and nonnesting partitions of types A and B - Mathematics > Combinatorics - Download this document for free, or read online. Document in PDF available to download.

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.

Author: ** Ricardo Mamede**

Source: https://arxiv.org/