The polynomial part of a restricted partition function related to the Frobenius problem

Matthias Beck, Ira M. Gessel, Takao Komatsu

Given a set of positive integers A = {a_1,...,a_n}, we study the number p_A (t) of nonnegative integer solutions (m_1,...,m_n) to m_1 a_1 + ... m_n a_n = t. We derive an explicit f…