Parity results for 13-regular partitions and broken 6-diamond partitions

Let $$b_{13}(n)$$ denote the number of partitions of n such that no parts are divisible by 13. In this paper, we shall prove several infinite families of congruence relations modulo 2 for $$b_{13}(n)$$ . In addition, we will give an elementary proof of the parity result on broken 6-diamond partitions, which was established by Radu and Sellers. We also find a new congruence relation modulo 2 for the number of broken 6-diamond partitions of n.