Bringmann and Lovejoy introduced a rank for overpartition pairs and
investigated its role in congruence properties of ppΛβ(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
ppΛβ(n). In this paper, we shall derive two Ramanujan-type identities and
some explicit congruences for ppΛβ(n). Moreover, we find three ranks as
combinatorial interpretations of the fact that ppΛβ(n) is divisible by
three for any n. We also construct infinite families of congruences for
ppΛβ(n) modulo 3, 5, and 9.Comment: 19 page