Overpartitions and real quadratic fields (Q1434345)

An overpartition of \(n\) is a partition such that the first occurrence of a part may be overlined. The author proves three theorems regarding overpartitions into distinct parts. One such theorem is as follows: Let \(a^+(n)\) denote the number of overpartitions of \(n\) into distinct parts that differ by at least 2 if the smaller part is overlined, with the largest part even. Likewise, let \(a^-(n)\) denote the number of overpartitions of \(n\) into distinct parts with largest part odd. Then the value of \(a^+(n)- a^-(n)\) depends on the canonical factorization of \(n\).