指数除数 Poset 的发生函数

Mathematica Pannonica Pub Date : 2024-06-13 DOI:10.1556/314.2024.00011

P. Haukkanen

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引用次数: 0

摘要

如果对于 𝑝𝑖 𝑛 的所有素除数，一个正整数的 𝑑𝑖 ∣ 𝑛𝑖 都是指数除数或 e-除数，那么这个正整数就是指数除数或 e-除数。此外，1 是 1 的 e-除数。很容易看出，ℤ+ 在 e-可分性关系下是一个正集。利用这一观察结果，我们可以证明算术函数的 e 卷积是正集的入射函数卷积的一个例子。我们还注意到，在这一过程中，同一性、单位和莫比乌斯函数都得到了保留。

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Incidence Functions of the Exponential Divisor Poset

A positive integer is said to be an exponential divisor or an e-divisor of if 𝑑𝑖 ∣ 𝑛𝑖 for all prime divisors 𝑝𝑖 of 𝑛. In addition, 1 is an e-divisor of 1. It is easy to see that ℤ+ is a poset under the e-divisibility relation. Utilizing this observation we show that e-convolution of arithmetical functions is an example of the convolution of incidence functions of posets. We also note that the identity, units and the Möbius function are preserved in this process.

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Mathematica Pannonica

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