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Theoretical analysis reveals novel modular congruences for odd and even part statistics in colored partitions, highlighting hidden arithmetic symmetries.
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.
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Baruah et al. (2026) studied this question.
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