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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

   

 

Extended admissible functions and Gaussian limiting distributions


Authors: Michael Drmota, Bernhard Gittenberger and Thomas Klausner
Journal: Math. Comp. 74 (2005), 1953-1966
MSC (2000): Primary 41A60; Secondary 68R05, 60F05, 05A16
Published electronically: March 14, 2005
MathSciNet review: 2164105
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Abstract: We consider an extension of Hayman's notion of admissibility to bivariate generating functions $f(z,u)$ that have the property that the coefficients $a_{nk}$ 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: http://dx.doi.org/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
Published electronically: March 14, 2005
Additional Notes: This work has been supported by the Austrian Science Foundation FWF, grant P16053-N05
Article copyright: © Copyright 2005 by the authors. All rights reserved.