, 22:311 | Cite as

A Distributive Lattice Structure Connecting Dyck Paths, Noncrossing Partitions and 312-avoiding Permutations

  • Elena Barcucci
  • Antonio Bernini
  • Luca Ferrari
  • Maddalena Poneti


In [Ferrari, L. and Pinzani, R.: Lattices of lattice paths. J. Stat. Plan. Inference 135 (2005), 77–92] a natural order on Dyck paths of any fixed length inducing a distributive lattice structure is defined. We transfer this order to noncrossing partitions along a well-known bijection [Simion, R.: Noncrossing partitions. Discrete Math. 217 (2000), 367–409], thus showing that noncrossing partitions can be endowed with a distributive lattice structure having some combinatorial relevance. Finally we prove that our lattices are isomorphic to the posets of 312-avoiding permutations with the order induced by the strong Bruhat order of the symmetric group.

Key Words

Dyck paths noncrossing partitions 312-avoiding permutations distributive lattice Bell and Catalan numbers strong Bruhat order 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Elena Barcucci
    • 1
  • Antonio Bernini
    • 1
  • Luca Ferrari
    • 2
  • Maddalena Poneti
    • 1
  1. 1.Dipartimento di Sistemi e InformaticaFirenzeItaly
  2. 2.Dipartimento di Scienze Matematiche ed InformaticheSienaItaly

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