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On maximal chains in the non-crossing partition lattice

โœ Scribed by Adin, Ron M.; Roichman, Yuval


Book ID
122275261
Publisher
Elsevier Science
Year
2014
Tongue
English
Weight
440 KB
Volume
125
Category
Article
ISSN
0097-3165

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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 num

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A matrix associated with the chromatic join of non-crossing partitions has been introduced by Tutte to generalise the Birkhoff-Lewis equations. A conjecturc is given for its determinant in terms of polynomials having the Beraha numbers among their roots. Corrcsponding results for join and meet on th