Explicit formulas for partition pairs and triples with 3-cores.

Let A 3 ( n ) (resp. B 3 ( n ) ) denote the number of partition pairs (resp. triples) of n where each partition is 3-core. By applying Ramanujan's ψ 1 1 formula and Bailey's ψ 6 6 formula, we find the explicit formulas for A 3 ( n ) and B 3 ( n ) . Using these formulas, we confirm a conjecture of Xia and establish many arithmetic identities satisfied by A 3 ( n ) and B 3 ( n ) . [ABSTRACT FROM AUTHOR]