The Ramanujan Journal

, Volume 46, Issue 1, pp 19–27 | Cite as

On \((\ell , m)\)-regular partitions with distinct parts

Article
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Accepted:

Abstract

Let \(a_{\ell ,m}(n)\) denote the number of \((\ell ,m)\)-regular partitions of a positive integer n into distinct parts, where \(\ell \) and m are relatively primes. In this paper, we establish several infinite families of congruences modulo 2 for \(a_{3,5}(n)\). For example,
$$\begin{aligned} a_{3, 5}\left(2^{6\alpha +4}5^{2\beta }n+\frac{ 2^{6\alpha +3}5^{2\beta +1}-1}{3}\right) \equiv 0 , \end{aligned}$$
where \(\alpha , \beta \ge 0\).

Keywords

Partition identities Theta-functions Partition congruences Regular partition 

Mathematics Subject Classification

11P83 05A17 
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Notes

Acknowledgements

The authors are thankful to the referee for useful suggestions which improved the quality of the paper.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of MathematicsPES College of EngineeringMandyaIndia
  2. 2.Department of MathematicsVSK UniversityBellaryIndia

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