论文标题
企业分区和Jordan构成功能
Coprime partitions and Jordan totient functions
论文作者
论文摘要
我们表明，虽然$ k $ parts的正整数$ n $的副本组成数量可以表示为$ \ mathbb {q} $ - jordan toctient函数的线性组合，但对于$ n $ to $ k $ parts而言，这是$ n $ n $ n $ n $ n $ n $ nike cocrime分区的可能性。我们还表明，$ n $ $ n $的数字$ p_k'（n）$ n $ k $ parts可以表示为$ \ mathbb {c} $ - jordan totient函数的线性组合，对于$ n $，对于$ n $，对于$ n $，且仅当$ k \ in \ in \ in \ in \ {2,3，3，3，，3，y和独特的方式时。最后，我们介绍了Jordan Tortient函数的一些概括，并表明$ P_K'（n）$始终可以表示为$ \ Mathbb {C} $ - 它们的线性组合。
We show that while the number of coprime compositions of a positive integer $n$ into $k$ parts can be expressed as a $\mathbb{Q}$-linear combinations of the Jordan totient functions, this is never possible for the coprime partitions of $n$ into $k$ parts. We also show that the number $p_k'(n)$ of coprime partitions of $n$ into $k$ parts can be expressed as a $\mathbb{C}$-linear combinations of the Jordan totient functions, for $n$ sufficiently large, if and only if $k\in \{2,3\}$ and in a unique way. Finally we introduce some generalizations of the Jordan totient functions and we show that $p_k'(n)$ can be always expressed as a $\mathbb{C}$-linear combinations of them.
