A generating functionology approach to a problem of Wilf

Authors:
Paweł Hitczenko;Cecil Rousseau;Carla D. Savage
Affiliations:
-;Department of Mathematical Sciences, University of Memphis, Memphis, TN;Department of Computer Science, North Carolina State University, Raleigh, NC
Venue:
Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
Year:
2002

Citing 4
Cited 0

Generating functionology

Generating functionology
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On the multiplicity of parts in a random partition

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Analytic Combinatorics

Analytic Combinatorics

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Abstract

Wilf posed the following problem: determine asymptotically as n → ∞ the probability that a randomly chosen part size in a randomly chosen composition of n has multiplicity m. One solution of this problem has been given by two of the authors . In this paper, we study this question using the techniques of generating functions and singularity analysis.