Overpartitions and singular overpartitions

Abstract

Singular overpartitions, which were defined by George Andrews, are overpartitions whose Frobenius symbols have at most one overlined entry in each row. In his paper, Andrews obtained interesting combinatorial results on singular overpartitions, one of which relates a certain type of singular overpartition with a subclass of overpartitions. In this paper, we provide a combinatorial proof of Andrews’s result, which answers one of his open questions.