Some Properties and Combinatorial Implications of Weighted Small Schr\"oder Numbers

zbMath1455.05004arXiv1912.00555MaRDI QIDQ5144725

Yu Hin (Gary) Au

Publication date: 19 January 2021

Full work available at URL: https://arxiv.org/abs/1912.00555

zbMATH Keywords

Catalan numberDyck pathSchröder numberNarayana numberSchröder pathplane rooted tree

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15)

Uses Software

• OEIS

Cites Work

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• Operads from posets and Koszul duality
• Identities involving weighted Catalan, Schröder and Motzkin paths
• Counting outerplanar maps
• Bijective recurrences concerning Schröder paths
• A classic proof of a recurrence for a very classical sequence
• Generalizing Narayana and Schröder numbers to higher dimensions
• Polygon dissections and standard Young tableaux
• Embedding structures associated with Riordan arrays and moment matrices
• Generalized small Schröder numbers
• Integer Sequences from Queueing Theory
• Hipparchus, Plutarch, Schroder, and Hough

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