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A bijection between noncrossing and nonnesting partitions of types A and B
The total number of noncrossing partitions of type is the th
Catalan number when , and the
binomial when , and these numbers coincide with the
correspondent number of nonnesting partitions. For type A, there are several
bijective proofs of this equality, being the intuitive map that locally
converts each crossing to a nesting 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.Comment: 11 pages, 11 figures. Inverse map described. Minor changes to correct
typos and clarify conten
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