Resumen de On the restricted partition function via determinants with Bernoulli polynomials. II

Mircea Cimpoeas

• Let r ≥ 1 be an integer, a = (a1, . . . , ar) a vector of positive integers, and let D ≥ 1 be a common multiple of a1, . . . , ar. We prove that if D = 1 or D is a prime number then the restricted partition function pa(n) := the number of integer solutions (x1, . . . , xr) to Pr j=1 ajxj = n, with x1 ≥ 0, . . . , xr ≥ 0, can be computed by solving a system of linear equations with coefficients that are values of Bernoulli polynomials and Bernoulli–Barnes numbers.