Riordan arrays and combinatorial sums
type: Item
instance of: scholarly article
title: Riordan arrays and combinatorial sums
zbMATH Open document ID: 0814.05003
DOI: 10.1016/0012-365X(92)00570-H
author: Renzo Sprugnoli
published in: Discrete Mathematics
publication date: 1994-11-03T00:00:00Z
review text: Enlarged abstract: The concept of a Riordan array, introduced under the name of renewal array in [\textit{D. G. Rogers}, Pascal triangles, Catalan numbers and renewal arrays, Discrete Math. 22, 301-310 (1978; Zbl 0398.05007)] and generalized to its present form in [\textit{L. W. Shapiro}, \textit{S. Getu}, \textit{W.-J. Woan} and \textit{L. C. Woodson}, The Riordan group, Discrete Appl. Math. 34, No. 1-3, 229-239 (1991; Zbl 0754.05010)], is used in a constructive way to find the generating function of many combinatorial sums. The generating function can then help us to obtain the closed form of the sum or its asymptotic value. Some examples of sums involving binomial coefficients and Stirling numbers are examined, together with an application of Riordan arrays to some walk problems.
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A10
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 11B73
zbMATH DE Number: 681672
zbMATH Keywords: renewal array
zbMATH Keywords: generating function
zbMATH Keywords: combinatorial sums
zbMATH Keywords: binomial coefficients
zbMATH Keywords: Stirling numbers
zbMATH Keywords: Riordan arrays
reviewed by: Timothy R. S. Walsh
MaRDI profile type: Publication
Wikidata QID: Q29012142
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DBLP publication ID: journals/dm/Sprugnoli94
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description: scientific article; zbMATH DE number 681672