CONGRUENCES MODULO 2 FOR CERTAIN PARTITION FUNCTIONS

Let (Formula presented.) denote the number of partitions of (Formula presented.) into parts that are not multiples of 3 or 5. We establish several infinite families of congruences modulo 2 for (Formula presented.). In the process, we also prove numerous parity results for broken 7-diamond partitions. © 2015 Australian Mathematical Publishing Association Inc