A generalization of the Farkas and Kra partition theorem for modulus 7 (Q1775545)

Consider partitions of natural numbers into parts such that multiples of 7 may be overlined. In a prior work [Contemp. Math. 251, 197--203 (2000; Zbl 1050.11086)], \textit{H. M. Farkas} and \textit{I. Kra} proved that the number of such partitions of \(2n\) into distinct even parts equals the number of partitions of \(2n+1\) into distinct odd parts. Using \(q\)-series identities, the author proves a theorem whose statement is quite complicated that greatly generalizes the earlier result of Farkas and Kra.