Riordan arrays and combinatorial sums. (English) Zbl 0814.05003

Enlarged abstract: The concept of a Riordan array, introduced under the name of renewal array in [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 [L. W. Shapiro, S. Getu, W.-J. Woan and 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.


05A15 Exact enumeration problems, generating functions
05A10 Factorials, binomial coefficients, combinatorial functions
05A19 Combinatorial identities, bijective combinatorics
11B73 Bell and Stirling numbers
Full Text: DOI


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