Arithmetic Properties of Overpartition Pairs
William Y. C. Chen and Bernard L.S. Lin
Abstract: Bringmann and Lovejoy introduced a rank for overpartition pairs and investigated its role in congruence properties of , 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 . In this paper, we derive two Ramanujan-type identities and some explicit congruences for . Moreover, we find three ranks as combinatorial interpretations of the fact that is divisible by three for any n. We also construct infinite families of congruences for modulo 3 and 5, and two congruence relations modulo 9.
AMS Classification : 05A17, 11P83
Keywords: overpartition pairs, rank of overpartition pairs, congruence, sum of squares