Riordan arrays, Łukasiewicz paths and Narayana polynomials

DOI10.1016/j.laa.2021.03.012zbMath1465.05004OpenAlexW3136839914MaRDI QIDQ2029864

Lin Yang, Sheng-Liang Yang

Publication date: 4 June 2021

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2021.03.012

zbMATH Keywords

Motzkin pathsNarayana numbersRiordan arraysSchröder pathsNarayana polynomialsŁukasiewicz paths

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) Permutations, words, matrices (05A05) Special sequences and polynomials (11B83) Matrices of integers (15B36)

Related Items (5)

Left multiplication operators on the Riordan group ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Diameter of io-decomposable Riordan graphs of the Bell type ⋮ On some properties of generalized Narayana numbers

Uses Software

• OEIS

Cites Work

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• Combinatorics of a generalized Narayana identity
• Combinatorics of Riordan arrays with identical \(A\) and \(Z\) sequences
• Identities derived from noncrossing partitions of type \(B\)
• The hitting time subgroup, Łukasiewicz paths and Faber polynomials
• Identities induced by Riordan arrays
• Sequence characterization of Riordan arrays
• Identities involving Narayana polynomials and Catalan numbers
• The Riordan group
• Some \(q\)-analogues of the Schröder numbers arising from combinatorial statistics on lattice paths
• Some combinatorial interpretations of \(q\)-analogs of Schröder numbers
• The Narayana distribution
• Catalan path statistics having the Narayana distribution
• Enumerating a class of lattice paths
• Counting lattice paths by Narayana polynomials
• Half of a Riordan array and restricted lattice paths
• Enumeration of Łukasiewicz paths modulo some patterns
• Bijections of Motzkin paths using shifted Riordan decompositions
• A bijection between ordered trees and 2-Motzkin paths and its many consequences
• A divisibility property for a subgroup of Riordan matrices
• Generating trees and proper Riordan arrays
• A bijective proof of the equation linking the Schröder numbers, large and small
• Riordan arrays, generalized Narayana triangles, and series reversion

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