On some infinite families of congruences for [j, k]-partitions into even parts distinct

Abstract

In this paper, we define the partition function pedj;kðnÞ; the number of [j, k]-partitions of n into even parts distinct, where none of the parts are congruent to j (mod k) (where k [ j 1Þ. We obtain many infinite families of congruences modulo powers of 2 for ped3;6ðnÞ and congruences modulo powers of 2 and 3 for ped9;18ðnÞ. For example, for all n 0 and a; b 0; ped9;18 2 34aþ4 72bþ1 ð7n þ sÞ þ 11 34aþ3 72bþ1 þ 1 4 � 0 (mod 16); where s ¼ 0; 2; 3; 4; 5; 6: Keywords Congruences Partitions with even parts distinct [j k]-partition