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eISSN 0454-8124
pISSN 1225-6951

### Article

Kyungpook Mathematical Journal 2021; 61(1): 49-59

Published online March 31, 2021

### Some Congruences for Andrews' Partition Function $EO¯(n)$

Utpal Pore and Syeda Noor Fathima*

Department of Mathematics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry - 605 014, India
e-mail : utpal.mathju@gmail.com and dr.fathima.sn@gmail.com

Received: March 14, 2019; Revised: October 7, 2020; Accepted: October 8, 2020

### Abstract

Recently, Andrews introduced partition functions$EO(n)$ and $EO¯(n)$ where the function $EO(n)$ denotes the number of partitions of n in which every even part is less than each odd part and the function $EO¯(n)$ denotes the number of partitions enumerated by $EO(n)$ 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 $EO¯(n)$. We give a simple proof of the first Ramanujan-type congruences $EO¯10n+8≡0 mod5$ given by Andrews.

Keywords: partitions, partitions with even parts below odd parts, congruences.