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## Restricted Partition Functions as Bernoulli and Euler Polynomials of Higher
Order

- Author(s): Rubinstein, Boris Y.
- Fel, Leonid G.
- et al.

## Published Web Location

https://arxiv.org/pdf/math/0304356.pdfNo data is associated with this publication.

## Abstract

Explicit expressions for restricted partition function $W(s,{\bf d}^m)$ and its quasiperiodic components $W_j(s,{\bf d}^m)$ (called {\em Sylvester waves}) 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.