Kyungpook Mathematical Journal 2021; 61(1): 49-59
Published online March 31, 2021
Copyright © Kyungpook Mathematical Journal.
Some Congruences for Andrews' Partition Function
Utpal Pore and Syeda Noor Fathima*
Department of Mathematics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry - 605 014, India
e-mail : email@example.com and firstname.lastname@example.org
Received: March 14, 2019; Revised: October 7, 2020; Accepted: October 8, 2020
Recently, Andrews introduced partition functions and where the function denotes the number of partitions of n in which every even part is less than each odd part and the function denotes the number of partitions enumerated by 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 . We give a simple proof of the first Ramanujan-type congruences given by Andrews.
Keywords: partitions, partitions with even parts below odd parts, congruences.