Catalan, Motzkin, and Riordan numbers
type: Item
instance of: scholarly article
title: Catalan, Motzkin, and Riordan numbers
zbMATH Open document ID: 0933.05002
DOI: 10.1016/S0012-365X(99)00054-0
author: Frank R. Bernhart
published in: Discrete Mathematics
publication date: 1999-09-02T00:00:00Z
review text: The article presents a unified overview of the Catalan and Motzkin numbers together with a third sequence called Riordan (ring) numbers [see \textit{J. Riordan}, J. Comb. Theory, Ser. A 19, 214-222 (1975; Zbl 0308.05115)], having wide range of applications. For these numbers diverse techniques are displayed, including direct combinatorial correspondences, recursions, generating function equations, difference triangles, Lagrange inversion, planar coloring schemes, and chromatic polynomials. The list of references contains 47 items.
reviewed by: Indulis Strazdins
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 05C30
Mathematics Subject Classification ID: 11B83
zbMATH DE Number: 1331466
zbMATH Keywords: Riordan numbers
zbMATH Keywords: Catalan numbers
zbMATH Keywords: Motzkin numbers
zbMATH Keywords: generating function
zbMATH Keywords: difference triangles
zbMATH Keywords: Lagrange inversion
zbMATH Keywords: planar coloring
zbMATH Keywords: chromatic polynomials
Wikidata QID: Q56442436
describes a project that uses: OEIS
MaRDI profile type: Publication
cites work: Hilbert series of fixed free algebras and noncommutative classical invariant theory
cites work: Q4013349
cites work: Six-Rings in Minimal Five-Color Maps
cites work: Q3958482
cites work: The book thickness of a graph
cites work: Chromatic Polynomials
cites work: Historical Note on a Recurrent Combinatorial Problem
cites work: Moments of Dyck paths
cites work: Embedding Graphs in Books: A Layout Problem with Applications to VLSI Design
cites work: Triangulated polygons and frieze patterns
cites work: A note on plane trees
cites work: Dyck path enumeration
cites work: Enumeration of ladder graphs
cites work: Restricted plane tree representations of four Motzkin-Catalan equations
cites work: Automorphisms on Catalan trees and bracketings
cites work: Motzkin numbers
cites work: Q5632617
cites work: Q3669422
cites work: Coloring Six-Rings
cites work: Counting Interval Graphs
cites work: Q3958468
cites work: Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associative products
cites work: A correspondence between ordered trees and noncrossing partitions
cites work: An introduction to chromatic polynomials
cites work: Q3819084
cites work: Enumeration of plane trees by branches and endpoints
cites work: Similarity relations on finite ordered sets
cites work: THE ENUMERATION OF A FAMILY OF LADDER GRAPHS
cites work: THE ENUMERATION OF A FAMILY OF LADDER GRAPHS PART II: SCHRODER AND SUPERCONNECTIVE RELATIONS
cites work: Rhyming schemes: crossings and coverings
cites work: A Catalan triangle
cites work: A short proof of an identity of Touchard's concerning Catalan numbers
cites work: Positive Definite Matrices and Catalan Numbers, Revisited
cites work: On the structure of the lattice of noncrossing partitions
cites work: An Elementary Evaluation of the Catalan Numbers
cites work: Q4774085
cites work: Q4834167
cites work: A Contribution to the Theory of Chromatic Polynomials
cites work: Q4050622
cites work: On the Birkhoff-Lewis equations
cites work: Q4324964
DBLP publication ID: journals/dm/Bernhart99
description: scientific article; zbMATH DE number 1331466