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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Extended admissible functions and Gaussian limiting distributions
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by Michael Drmota, Bernhard Gittenberger and Thomas Klausner PDF
Math. Comp. 74 (2005), 1953-1966

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
  • MR Author ID: 59890
  • 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
  • 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
  • © Copyright 2005 by the authors. All rights reserved.
  • Journal: Math. Comp. 74 (2005), 1953-1966
  • MSC (2000): Primary 41A60; Secondary 68R05, 60F05, 05A16
  • DOI: https://doi.org/10.1090/S0025-5718-05-01744-8
  • MathSciNet review: 2164105