Ricardo Mamede
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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)
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https://doi.org/10.46298/dmtcs.2686
A bijection between noncrossing and nonnesting partitions of types A and B
Authors: Ricardo Mamede 1
0000-0002-9264-6604
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 $\Psi =A_{n-1}$, 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.
Non-crossing partitions for classical reflection groups
2 Documents citing this article
Source : OpenCitations
2012, H C++ Programming, Combinatorics Of Set Partitions, pp. 547-564, 10.1201/b12691-22.
Conflitti, Alessandro; Mamede, Ricardo, 2011, On Noncrossing And Nonnesting Partitions Of Type D, Annals Of Combinatorics, 15, 4, pp. 637-654, 10.1007/s00026-011-0114-5.