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

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Abstract

For any positive integer ℓ, let B ℓ (n) denotes the number of ℓ-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).

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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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Authors and Affiliations

  1. Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh, 791112, Arunachal Pradesh, India

    Nipen Saikia & Chayanika Boruah

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  1. Nipen Saikia
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  2. Chayanika Boruah
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Correspondence to Nipen Saikia.

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Saikia, N., Boruah, C. Congruences of ℓ − Regular Partition Triples for ℓ ∈{2, 3, 4, 5}. Acta Math Vietnam 42, 551–561 (2017). https://doi.org/10.1007/s40306-017-0206-3

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  • DOI: https://doi.org/10.1007/s40306-017-0206-3

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