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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Bibliographic Details
Published in:Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings vol. AQ,...; no. Proceedings; pp. 453 - 478
Main Authors: Drmota, Michael, Gittenberger, Bernhard, Morgenbesser, Johannes F.
Format: Journal Article Conference Proceeding
Language:English
Published: DMTCS 01.01.2012
Discrete Mathematics and Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science
Series:DMTCS Proceedings
Subjects:
[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
Online Access:Get full text
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Summary: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