An Addition Theorem for the Elementary Abelian Group of Type (p, p).
Let be a non-empty subset of positive integers. A partition of a positive integer into is a finite nondecreasing sequence of positive integers in with repetitions allowed such that . Here we apply Pólya’s enumeration theorem to find the number of partitions of into , and the number of distinct partitions of into . We also present recursive formulas for computing and .
Let d(n) stand for the Dirichlet divisor function. We give an asymptotic formula for with the help of the circle method.