Some Overpartition k-tuple Congruence Properties

Each of the elements of this list is itself a partition, and the numbers in each partition are referred to as parts . As one may clearly deduce, the larger the number, the more partitions it has. Also of note is the fact that is the same as , that is, order is not accounted for. Typically, the parts of a partition are written in nonincreasing order. It is also commonly accepted that the function , where is a positive integer, is the function which counts the number of partitions of .