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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On congruence properties of $p(n,m)$


Author: Brandt Kronholm
Journal: Proc. Amer. Math. Soc. 133 (2005), 2891-2895
MSC (2000): Primary 05A17, 11P83
Published electronically: April 25, 2005
MathSciNet review: 2159766
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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.


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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
Email: kronholm@math.psu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07972-4
PII: S 0002-9939(05)07972-4
Keywords: Partition, congruence, generating function, Ramanujan
Received by editor(s): June 9, 2004
Published electronically: April 25, 2005
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.