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Partitions in 3 colours

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Abstract

We study \(p_3(n)\), the number of partitions of n in three colours, and derive congruences for \(p_3(n)\) modulo high powers of 3.

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References

  1. Hirschhorn, M.D.: The Power of \(q\), Chapters 5 and 6. Springer (to appear)

  2. Hirschhorn, M.D., Hunt, D.C.: A simple proof of the Ramanujan conjecture for powers of 5. J. Reine Angew. Math. 326, 1–17 (1981)

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Acknowledgments

The congruences (1.6) and (1.7) were discovered by F. Garvan.

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Authors and Affiliations

  1. School of Mathematics and Statistics, UNSW, Sydney, 2052, Australia

    Michael D. Hirschhorn

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  1. Michael D. Hirschhorn
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Correspondence to Michael D. Hirschhorn.

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Hirschhorn, M.D. Partitions in 3 colours. Ramanujan J 45, 399–411 (2018). https://doi.org/10.1007/s11139-016-9835-8

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  • DOI: https://doi.org/10.1007/s11139-016-9835-8

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