Restricted partition functions as Bernoulli and Eulerian polynomials of higher order
Restricted partition functions as Bernoulli and Eulerian polynomials of higher order
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受限配分函数为高阶伯努利多项式和欧拉多项式
DOI：
10.1007/s11139-006-8479-5
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
L. Fel
中科院分区：
文献类型：
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作者：
B. Rubinstein;L. Fel
导出了一组正整数 dm= {d1,d2, ...,dm} 的受限配分函数 W(s,dm) 及其准周期分量 Wj(s,dm) （称为西尔维斯特波）的显式表达式。这些公式以具有周期系数的高阶伯努利多项式和欧拉多项式的有限和的形式表示。建立了西尔维斯特波的一种新颖的递归关系。讨论了计算有限群的代数独立齐次多项式不变量的应用。
Explicit expressions for restricted partition functionW(s,dm) and its quasiperiodic componentsWj(s,dm) (calledSylvester waves) for a set of positive integersdm= {d1,d2, ...,dm} are derived. The formulas are represented in a form of a finite sum over Bernoulli and Eulerian 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 finite groups is discussed.