推广的Mõbius反转公式

郗平, 易媛

数学学报 ›› 2009, Vol. 52 ›› Issue (6) : 1135-1140.

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数学学报 ›› 2009, Vol. 52 ›› Issue (6) : 1135-1140. DOI: 10.12386/A2009sxxb0141
论文

推广的Mõbius反转公式

    郗 平, 易 媛
作者信息 +

On Generalized Mõbius Inversion Formulae

    Ping XI, Yuan YI
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文章历史 +

摘要

讨论了正整数集上 的更一般形式的Mõbius变换, 给出了一组对偶的推广形式的Mõbius反转公式, 并在此基础上获得了关于k次除数函数以及中心二项式系数的Mõbius 变换的一些性质. 另外还对一个已有的结果, 即本文定理的一个特殊情形给出了一个简化的直接证明.  

Abstract

In this paper,    a general Mõbius transform on  is discussed, and a pair of dual Mõbius inversion formulae are given, based on which some properties of the Mõbius transforms involving the k-th order divisor function and central binomial coefficients are obtained. A directly simplified proof of a known result, as a special case of our theorem, is also given.  

关键词

Mõbius反转公式 / k次除数函数 / 中心二项式系数

Key words

Mõbius inversion formula / k-th order divisor function / central binomial coefficient

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郗平, 易媛. 推广的Mõbius反转公式. 数学学报, 2009, 52(6): 1135-1140 https://doi.org/10.12386/A2009sxxb0141
Ping XI, Yuan YI. On Generalized Mõbius Inversion Formulae. Acta Mathematica Sinica, Chinese Series, 2009, 52(6): 1135-1140 https://doi.org/10.12386/A2009sxxb0141

参考文献



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基金

国家自然科学基金资助项目(10601039)

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