Difference of the sum of diverse parts of some colored partitions

Abstract

Recently, Andrews and Ghosh Dastidar (Ramanujan J. 69, Art. No. 26, 2026) studied two interesting partition statistics, namely, SOME(n) and DSOME(n), where SOME(n) is the sum of all the odd parts in the partitions of n minus the sum of all the even parts, and DSOME(n) is the sum of all the odd parts in the partitions of n into distinct parts minus the sum of all the even parts. They expressed the generating functions of SOME(n) and DSOME(n) in terms of q-series and found several interesting congruences modulo 4 and 5. In this paper, we explore similar statistics for some colored partitions which also satisfy some beautiful congruences.