Abstract

Explicit expressions for restricted partition function $W$ and its quasiperiodic components $W_j$ for a set of positive integers ${\bf d}^m = \{d_1, d_2,..., d_m\}$ are derived. The formulas are represented in a form of a finite sum over Bernoulli and Euler polynomials of higher order with periodic coefficients. A novel recursive relation for the Sylvester waves is established. Application to counting algebraically independent homogeneous polynomial invariants of the finite groups is discussed.