Arithmetic Properties of Overpartition Pairs

الأصل · EN

Bringmann and Lovejoy introduced a rank for overpartition pairs and investigated its role in congruence properties of pp(n), the number of overpartition pairs of n. In particular, they applied the theory of Klein forms to show that there exist many Ramanujan-type congruences for the number pp(n). In this paper, we shall derive two Ramanujan-type identities and some explicit congruences for pp(n). Moreover, we find three ranks as combinatorial interpretations of the fact that pp(n) is divisible by three for any n. We also construct infinite families of congruences for pp(n) modulo 3, 5, and 9.