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Acta Mathematica Vietnamica

, Volume 42, Issue 3, pp 551–561 | Cite as

Congruences of − Regular Partition Triples for ∈{2, 3, 4, 5}

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Abstract

For any positive integer , let B (n) denotes the number of -regular partition triples of a positive integer n. By employing q −series identities, we prove infinite family of arithmetic identities and congruences modulo 4 for B 2(n), modulo 2 and 9 for B 3(n), modulo 2 for B 4(n) and modulo 2 and 5 for B 5(n).

Keywords

-regular partition Partition triples Partition congruence q −series identities Ramanujan’s theta-functions 

Mathematics Subject Classification (2010)

11P83 05A15 05A17 

Notes

Acknowledgments

The first author (N. Saikia) is thankful to Council of Scientific and Industrial Research of India for partially supporting the research work under the Research Scheme No. 25(0241)/15/EMR-II (F. No. 25(5498)/15).

The authors thank anonymous referee for his/her valuable suggestions and comments.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2017

Authors and Affiliations

  1. 1.Department of MathematicsRajiv Gandhi UniversityDoimukhIndia

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