Some identities on the Catalan, Motzkin and Schröder numbers

DOI10.1016/j.dam.2007.11.014zbMath1148.05011OpenAlexW1977751406MaRDI QIDQ948698

Wei-Jun Yan, Eva Y. P. Deng

Publication date: 17 October 2008

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

Full work available at URL: https://doi.org/10.1016/j.dam.2007.11.014

zbMATH Keywords

Catalan numberMotzkin numberRiordan groupidentitySchröder number

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65)

Related Items (11)

Arithmetic into geometric progressions through Riordan arrays ⋮ Half of a Riordan array and restricted lattice paths ⋮ Determinant identities for the Catalan, Motzkin and Schröder numbers ⋮ Unnamed Item ⋮ Minors of a class of Riordan arrays related to weighted partial Motzkin paths ⋮ A relation between Schröder paths and Motzkin paths ⋮ Restricted inversion sequences and enhanced 3-noncrossing partitions ⋮ Some inverse relations determined by Catalan matrices ⋮ Combinatorial identities related to \(2 \times 2\) submatrices of recursive matrices ⋮ Identities from representation theory ⋮ A combinatorial bijection on \(k\)-noncrossing partitions

Uses Software

• OEIS

Cites Work

• Unnamed Item
• Unnamed Item
• The Riordan group
• Pascal triangles, Catalan numbers and renewal arrays
• Bijective recurrences concerning Schröder paths
• Catalan, Motzkin, and Riordan numbers
• Riordan arrays and combinatorial sums
• Sone new inverse series relations
• A bijection between ordered trees and 2-Motzkin paths and its many consequences
• Riordan arrays and the Abel-Gould identity
• Inverse Relations and Combinatorial Identities
• Motzkin numbers

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