Three Simple Reduction Formulas for the Denumerant Functions

Let A be a nonempty set of positive integers. The restricted partition function pA(n) denotes the number of partitions of n with parts in A. When the elements in A are pairwise relatively prime positive integers, Ehrhart, Sert\"oz-\"Ozl\"uk, and Brown-Chou-Shiue derived three reduction formulas for pA(n) for A with three parameters. We extend their findings for general A using the Bernoulli-Barnes polynomials.