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Restricted Partition Functions as Bernoulli and Euler Polynomials of Higher Order

Boris Y. Rubinstein·Leonid G. Fel
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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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Boris Y. Rubinstein, Leonid G. Fel. 2003-05-16. Restricted Partition Functions as Bernoulli and Euler Polynomials of Higher Order. https://arxiv.org/abs/math/0304356

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