On the identities of modulo-pp partitions

Some identities between partitions and compositions were obtained in the literature. As a natural extension, we introduce and study modulo-pp partitions, where pp is a positive integer. Moreover, several recurrence relations and some sufficient conditions for the existence of modulo-pp partitions are given, respectively. In addition, we obtain some identities of modulo-pp partitions. In the end, using the properties of a binary tree, we provide a method to determine modulo-pp partitions.