Andrews and El Bachraoui establish modulo-4 criteria for Ramanujan-type progressions in S1(q), overpartition counts for the even companion, and quintic self-similarity plus quadratic form conditions for the odd companion's coefficients.
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On a two-color partition series and its companions
Andrews and El Bachraoui establish modulo-4 criteria for Ramanujan-type progressions in S1(q), overpartition counts for the even companion, and quintic self-similarity plus quadratic form conditions for the odd companion's coefficients.