Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Some Congruences for Andrews' Partition Function ${\bar{\mathcal{EO}}}$(n)

  • Pore, Utpal (Department of Mathematics, Ramanujan School of Mathematical Sciences, Pondicherry University) ;
  • Fathima, Syeda Noor (Department of Mathematics, Ramanujan School of Mathematical Sciences, Pondicherry University)
  • Received : 2019.03.14
  • Accepted : 2020.10.08
  • Published : 2021.03.31
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Abstract

Recently, Andrews introduced partition functions ����(n) and ${\bar{\mathcal{EO}}}$(n) where the function ����(n) denotes the number of partitions of n in which every even part is less than each odd part and the function ${\bar{\mathcal{EO}}}$(n) denotes the number of partitions enumerated by ����(n) in which only the largest even part appears an odd number of times. In this paper we obtain some congruences modulo 2, 4, 10 and 20 for the partition function ${\bar{\mathcal{EO}}}$(n). We give a simple proof of the first Ramanujan-type congruences ${\bar{\mathcal{EO}}}$ (10n + 8) ≡ 0 (mod 5) given by Andrews.

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References

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