Combinatorial matrices derived from generalized Motzkin paths

DOI10.1007/s13226-021-00096-7zbMath1478.05016OpenAlexW3168679112MaRDI QIDQ2243093

Lin Yang, Sheng-Liang Yang

Publication date: 10 November 2021

Published in: Indian Journal of Pure \& Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13226-021-00096-7

zbMATH Keywords

generating functionCatalan numbersMotzkin numbersSchröder numbersRiordan arraygeneralized Motzkin path

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Permutations, words, matrices (05A05) Matrices of integers (15B36)

Uses Software

• OEIS

Cites Work

• Combinatorics of Riordan arrays with identical \(A\) and \(Z\) sequences
• Counting lattice paths with four types of steps
• Identities induced by Riordan arrays
• Skew Dyck paths
• The relevant prefixes of coloured Motzkin walks: an average case analysis
• Sequence characterization of Riordan arrays
• The Riordan group
• A Catalan triangle
• Underdiagonal lattice paths with unrestricted steps
• Riordan arrays and combinatorial sums
• Half of a Riordan array and restricted lattice paths
• A divisibility property for a subgroup of Riordan matrices
• A generalization of the \(k\)-bonacci sequence from Riordan arrays
• Enumeration via ballot numbers
• Schröder matrix as inverse of Delannoy matrix
• Three Hoppy path problems and ternary paths
• On Some Alternative Characterizations of Riordan Arrays
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