A distributive lattice structure connecting Dyck paths, noncrossing partitions and 312-avoiding permutations

DOI10.1007/s11083-005-9021-xzbMath1096.06007OpenAlexW2089049012MaRDI QIDQ2494390

Maddalena Poneti, Elena Barcucci, Antonio Bernini, Luca Ferrari

Publication date: 26 June 2006

Published in: Order (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11083-005-9021-x

zbMATH Keywords

distributive latticeBell numbersDyck pathsCatalan numbersnoncrossing partitions312-avoiding permutationsstrong Bruhat order

Mathematics Subject Classification ID

Partitions of sets (05A18) Combinatorics of partially ordered sets (06A07) Structure and representation theory of distributive lattices (06D05)

Related Items (10)

The pruning-grafting lattice of binary trees ⋮ The rank enumeration of certain parabolic non-crossing partitions ⋮ The phagocyte lattice of Dyck words ⋮ Cellular resolutions of ideals defined by nondegenerate simplicial homomorphisms ⋮ A Heyting algebra on Dyck paths of type \(A\) and \(B\) ⋮ Some combinatorics related to central binomial coefficients: Grand-Dyck paths, coloured noncrossing partitions and signed pattern avoiding permutations ⋮ The weak order on pattern-avoiding permutations ⋮ Noncrossing partitions and Bruhat order ⋮ Permutations and pairs of Dyck paths ⋮ Motzkin subposets and Motzkin geodesics in Tamari lattices.

Uses Software

• OEIS

Cites Work

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• The matrix of chromatic joins and the Temperley-Lieb algebra.
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• Vexillary involutions are enumerated by Motzkin numbers
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• Generating trees and the Catalan and Schröder numbers
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• Bruhat lattices, plane partition generating functions, and minuscule representations
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• Lattices of lattice paths
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• Generalized pattern avoidance
• An area-to-inv bijection between Dyck paths and 312-avoiding permutations
• Permutations with restricted patterns and Dyck paths
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