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Extended admissible functions and Gaussian limiting distributions
Author(s):
Michael
Drmota;
Bernhard
Gittenberger;
Thomas
Klausner.
Journal:
Math. Comp.
74
(2005),
1953-1966.
MSC (2000):
Primary 41A60;
Secondary 68R05, 60F05, 05A16
Posted:
March 14, 2005
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Abstract:
We consider an extension of Hayman's notion of admissibility to bivariate generating functions  that have the property that the coefficients  satisfy a central limit theorem. It is shown that these admissible functions have certain closure properties. Thus, there is a large class of functions for which it is possible to check this kind of admissibility automatically. This is realized with help of a MAPLE program that is also presented. We apply this concept to various combinatorial examples.
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Additional Information:
Michael
Drmota
Affiliation:
Department of Discrete Mathematics and Geometry, Technische Universität Wien, Wiedner Hauptstraße 8-10/104, A-1040 Wien, Austria
Email:
drmota@dmg.tuwien.ac.at
Bernhard
Gittenberger
Affiliation:
Department of Discrete Mathematics and Geometry, Technische Universität Wien, Wiedner Hauptstraße 8-10/104, A-1040 Wien, Austria
Email:
gittenberger@dmg.tuwien.ac.at
Thomas
Klausner
Affiliation:
Department of Discrete Mathematics and Geometry, Technische Universität Wien, Wiedner Hauptstraße 8-10/104, A-1040 Wien, Austria
Email:
klausner@dmg.tuwien.ac.at
DOI:
10.1090/S0025-5718-05-01744-8
PII:
S 0025-5718(05)01744-8
Keywords:
Hayman admissible functions,
central limit theorem,
automatic expansion,
combinatorial enumeration
Received by editor(s):
August 19, 2003,
Received by editor(s) in revised form:
June 22, 2004.
Posted:
March 14, 2005
Additional Notes:
This work has been supported by the Austrian Science Foundation FWF, grant P16053-N05
Copyright of article:
Copyright
2005,
by the authors. All rights reserved.
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