Restricted Partition Functions as Bernoulli and Euler Polynomials of Higher Order
Open Access Publications from the University of California

## 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.pdf
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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.

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