Infinite Systems of Functional Equations and Gaussian Limiting Distributions

In this paper infinite systems of functional equations in finitely or infinitely many random variables arising in combinatorial enumeration problems are studied. We prove sufficient conditions under which the combinatorial random variables encoded in the generating function of the system tend to a f...

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Vydané v:Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings vol. AQ,...; číslo Proceedings; s. 453 - 478
Hlavní autori: Drmota, Michael, Gittenberger, Bernhard, Morgenbesser, Johannes F.
Médium: Journal Article Konferenčný príspevok..
Jazyk:English
Vydavateľské údaje: DMTCS 01.01.2012
Discrete Mathematics and Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science
Edícia:DMTCS Proceedings
Predmet:
[info.info-cg] computer science [cs]/computational geometry [cs.cg]
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
[info.info-ds] computer science [cs]/data structures and algorithms [cs.ds]
[math.math-co] mathematics [math]/combinatorics [math.co]
central limit theorem
Combinatorics
Computational Geometry
Computer Science
Data Structures and Algorithms
Discrete Mathematics
functional equation
generating functions
Mathematics
singularity analysis
singularity analysis
generating functions
central limit theorem
functional equation
ISSN:1365-8050, 1462-7264, 1365-8050
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Popis
Shrnutí:In this paper infinite systems of functional equations in finitely or infinitely many random variables arising in combinatorial enumeration problems are studied. We prove sufficient conditions under which the combinatorial random variables encoded in the generating function of the system tend to a finite or infinite dimensional limiting distribution.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.3012