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arXiv · 2404.13989

Three Simple Reduction Formulas for the Denumerant Functions

Feihu Liu·Guoce Xin·Chen Zhang
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Abstract

Let $A$ be a nonempty set of positive integers. The restricted partition function $p_A(n)$ denotes the number of partitions of $n$ with parts in $A$. When the elements in $A$ are pairwise relatively prime positive integers, Ehrhart, Sertöz-Özlük, and Brown-Chou-Shiue derived three reduction formulas for $p_A(n)$ for $A$ with three parameters. We extend their findings for general $A$ using the Bernoulli-Barnes polynomials.

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Feihu Liu, Guoce Xin, Chen Zhang. 2024-04-24. Three Simple Reduction Formulas for the Denumerant Functions. https://doi.org/10.1007/s11139-024-00955-x

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