Ricardo Mamede

A bijection between noncrossing and nonnesting partitions of types A and B
dmtcs:2686 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2009,
DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)

https://doi.org/10.46298/dmtcs.2686
A bijection between noncrossing and nonnesting partitions of types A and BArticle
Authors: Ricardo Mamede ^{1}
0000000292646604
Ricardo Mamede
1 Department of Mathematics
The total number of noncrossing partitions of type $\Psi$ is the $n$th Catalan number $\frac{1}{ n+1} \binom{2n}{n}$ when $\Psi =A_{n1}$, and the binomial coefficient $\binom{2n}{n}$ 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 paper 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.
Chapman and Hall/CRC eBooks, H C++ Programming, pp. 547564, 2012, 10.1201/b1269122.
Alessandro Conflitti;Ricardo Mamede, 2011, On Noncrossing and Nonnesting Partitions of Type D, arXiv (Cornell University), 15, 4, pp. 637654, 10.1007/s0002601101145.