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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On congruence properties of $p(n,m)$
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by Brandt Kronholm PDF
Proc. Amer. Math. Soc. 133 (2005), 2891-2895 Request permission

Abstract:

In the late 19th century, Sylvester and Cayley investigated the properties of the partition function $p(n,m)$. This function enumerates the partitions of a non-negative integer $n$ into exactly $m$ parts. Here we investigate the congruence properties of such functions and we obtain several infinite classes of Ramanujan-type congruences.
References
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  • A. O. L. Atkin, Proof of a conjecture of Ramanujan, Glasgow Math. J. 8 (1967), 14–32. MR 205958, DOI 10.1017/S0017089500000045
  • H. Gupta, E. E. Gwyther and J. C. P. Miller, Tables of Partitions, Royal Soc. Math. Tables, Vol. 4, Cambridge University Press, Cambridge, 1958.
  • Ken Ono, Distribution of the partition function modulo $m$, Ann. of Math. (2) 151 (2000), no. 1, 293–307. MR 1745012, DOI 10.2307/121118
  • S. Ramanujan, Collected Papers, Cambridge University Press, London, 1927; reprinted: A. M. S. Chelsea, 2000 with new preface and extensive commentary by B. Berndt.
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Additional Information
  • Brandt Kronholm
  • Affiliation: Department of Mathematics, Penn State University, University Park, Pennsylvania 16802
  • Address at time of publication: Department of Mathematics, University at Albany, Albany, New York 12222
  • MR Author ID: 766642
  • Email: kronholm@math.psu.edu
  • Received by editor(s): June 9, 2004
  • Published electronically: April 25, 2005
  • Communicated by: David E. Rohrlich
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 2891-2895
  • MSC (2000): Primary 05A17, 11P83
  • DOI: https://doi.org/10.1090/S0002-9939-05-07972-4
  • MathSciNet review: 2159766