The Ramanujan Journal

, Volume 30, Issue 3, pp 425–436 | Cite as

Generalized congruence properties of the restricted partition function p(n,m)

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Abstract

Ramanujan-type congruences for the unrestricted partition function p(n) are well known and have been studied in great detail. The existence of Ramanujan-type congruences are virtually unknown for p(n,m), the closely related restricted partition function that enumerates the number of partitions of n into exactly m parts. Let ℓ be any odd prime. In this paper we establish explicit Ramanujan-type congruences for p(n,ℓ) modulo any power of that prime ℓ α . In addition, we establish general congruence relations for p(n,ℓ) modulo ℓ α for any n.

Keywords

Partition Congruence Generating function Ramanujan 

Mathematics Subject Classification

05A17 11P83 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Whittier CollegeWhittierUSA

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