New parity results for broken 11-diamond partitions

The notation of broken k-diamond partitions was introduced in 2007 by Andrews and Paule. For a fixed positive integer k, let Delta(k)(n) denote the number of broken k-diamond partitions of n. Recently, Radu and Sellers established numerous congruence properties for (2k +1)-cores by using the theory of modular forms, where k = 2, 3, 5, 6, 8, 9, 11. Employing their congruences for (2k + 1)-cores, Radu and Sellers obtained a number of nice parity results for Delta(k)(n). In particular, they proved that for n >= 0, Delta(11)(46n + r) equivalent to 0 (mod 2), where r is an element of {11, 15, 21, 23, 29, 31, 35, 39, 41, 43, 45}. In this paper, we derive several new infinite families of congruences modulo 2 for Delta(11)(n) by using an identity given by Chan and Toh, and the p-dissection of Ramanujan's theta function f(1) due to Cui and Gu. For example, we prove that for n >= 0 and k, alpha >= 1, Delta(11)(2(3 alpha-2) x 23(k)n +2(3 alpha-2)s x 23(k-1) + 1) equivalent to 0 (mod 2), where s is an element of {5,7, 10, 11, 14, 15, 17, 19, 20, 21, 22}. This generalizes the parity results for Delta(11)(n) discovered by Radu and Sellers. (C) 2014 Elsevier Inc. All rights reserved.