Congruences for Partition Quadruples with t-Cores

Abstract

Let Ct(n) denote the number of partition quadruples of n with t-cores for t = 3,5,7,25. We establish some Ramanujan type congruences modulo 5, 7, 8 for Ct(n). For example, n ≥ 0, we have

$$ \begin{array}{@{}rcl@{}} C_{5}(5n+4)&\equiv& 0\pmod{5},\\ C_{7}(7n+6)&\equiv& 0\pmod{7},\\ C_{3}(16n+14)&\equiv& 0\pmod{8}. \end{array} $$

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Correspondence to M. S. Mahadeva Naika.

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Naika, M.S.M., Nayaka, S.S. Congruences for Partition Quadruples with t-Cores. Acta Math Vietnam 45, 795–806 (2020). https://doi.org/10.1007/s40306-019-00356-z

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Keywords

  • Congruences
  • Partition quadruples
  • t-core partition

Mathematics Subject Classification (2010)

  • 11P81
  • 11P83