New congruences for broken k-diamond partitions

Broken k-diamond partitions were introduced by Andrews and Paule. Let \({\Delta }_{k}(n)\) ${\mathrm{\Delta }}_k(n)$ denote the number of broken \(k\) $k$ -diamond partitions of \(n\) $n$ . In 2015, by using the theory of Ramanujan’s theta function, Ahmed and Baruah established some congruences modulo 2 for \({\Delta }_{7}(n)\) ${\mathrm{\Delta }}_7(n)$ . In this note, we continue to study the congruence properties of \({\Delta }_{7}(n)\) ${\mathrm{\Delta }}_7(n)$ . By using the theory of modular forms, we generalize the congruences proved by Ahmed and Baruah. In addition, we also find two congruences modulo 2 for \({\Delta }_{23}(n)\) ${\mathrm{\Delta }}_{23}(n)$ .