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http://dx.doi.org/10.5666/KMJ.2021.61.1.49

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)
Publication Information
Kyungpook Mathematical Journal / v.61, no.1, 2021 , pp. 49-59 More about this Journal
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.
Keywords
partitions with even parts below odd parts; congruences;
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  • Reference
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