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Chains in the lattice of noncrossing partitions

✍ Scribed by Paul H. Edelman; Rodica Simion

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
735 KB
Volume
126
Category
Article
ISSN
0012-365X

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✦ Synopsis

The lattice of noncrossing set partitions is known to admit an R-labeling. Under this labeling, maximal chains give rise to permutations.

We discuss structural and enumerative properties of the lattice of noncrossing partitions, which pertain to a new permutation statistic, m(a), defined as the number of maximal chains labeled by 0. Miibius inversion results and related facts about the lattice of unrestricted set partitions are also presented.

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