Catalan pairs: a relational-theoretic approach to Catalan numbers

DOI10.1016/j.aam.2010.02.004zbMath1221.05016arXiv0901.3509OpenAlexW2047947538WikidataQ60692090 ScholiaQ60692090MaRDI QIDQ1958940

Filippo Disanto, Luca Ferrari, Renzo Pinzani, Simone Rinaldi

Publication date: 30 September 2010

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.3509

zbMATH Keywords

posetrepresentationbinary relationCatalan numberspattern avoidanceplane treeordered pairperfect noncrossing matchingpattern avoiding permutation312 avoiding permutation

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Permutations, words, matrices (05A05) Combinatorics of partially ordered sets (06A07)

Related Items (6)

Generation and enumeration of some classes of interval orders ⋮ Catalan structures and Catalan pairs ⋮ Catalan pairs and Fishburn triples ⋮ Refining the bijections among ascent sequences, \((2+2)\)-free posets, integer matrices and pattern-avoiding permutations ⋮ Refining the bijections among ascent sequences, (2+2)-free posets, integer matrices and pattern-avoiding permutations ⋮ Enumeration of some classes of pattern avoiding matchings, with a glimpse into the matching pattern poset

Uses Software

• OEIS

Cites Work

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• On Whitney numbers of the order ideals of generalized fences and crowns
• A correspondence between ordered trees and noncrossing partitions
• A Catalan triangle
• Some enumeration problems for similarity relations
• On the rank polynomial of the lattice of order ideals of fences and crowns
• Multiple pattern avoidance with respect to fixed points and excedances
• Permutations with forbidden subsequences and a generalized Schröder number
• No four subsets forming an \(N\)
• Intransitive indifference with unequal indifference intervals
• Enumeration of Posets Generated by Disjoint Unions and Ordinal Sums
• Extrapolation when very little is known about the source
• Generalized pattern avoidance

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