A General Asymptotic Scheme for the Analysis of Partition Statistics. (November 2014)

• Record Type: Journal Article
• Authors: GRABNER, PETER J.; KNOPFMACHER, ARNOLD; WAGNER, STEPHAN; Broutin, Nicolas; Fill, James Allen; Nebel, Markus; Ward, Mark Daniel
• Is Part Of: Combinatorics, probability and computing. Volume 23:Number 6(2014:Nov.)
• Page Start: 1057
• Page End: 1086
• Publication Date: 2014-11
• Subjects: Combinatorial analysis -- Periodicals; Probabilities -- Periodicals; Computer science -- Mathematics -- Periodicals; 511.6
• DOI: 10.1017/S0963548314000418
• Languages: English
• ISSNs: 0963-5483

Abstract

<abstract abstract-type="normal"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>We consider statistical properties of random integer partitions. In order to compute means, variances and higher moments of various partition statistics, one often has to study generating functions of the form <italic>P(x)F(x)</italic>, where <italic>P(x)</italic> is the generating function for the number of partitions. In this paper, we show how asymptotic expansions can be obtained in a quasi-automatic way from expansions of <italic>F(x)</italic> around <italic>x</italic> = 1, which parallels the classical singularity analysis of Flajolet and Odlyzko in many ways. Numerous examples from the literature, as well as some new statistics, are treated via this methodology. In addition, we show how to compute further terms in the asymptotic expansions of previously studied partition statistics.</p> </abstract>