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 ORCID1

  • 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.


Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: Root systems,noncrossing partitions,nonnesting partitions,bijection,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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