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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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