Infinite families of arithmetic identities and congruences for bipartitions with 3-cores

Let A(3) (n) denote the number of bipartitions of n that are 3-cores. By employing Ramanujan's simple theta function identities, we prove that A(3)(2n + 1) = 1/3 sigma(6n + 5), where sigma(n) denotes the sum of the positive divisors of n. We also find several infinite families of arithmetic identities and congruences for A(3)(n), which include generalizations of some recent results on A(3)(n) by B.L.S. Lin (2014) [6]. (C) 2014 Elsevier Inc. All rights reserved.