标题： 贪婪正则卷积 显示英文标题

标题： Greedy Regular Convolutions

摘要： 我们引入了一类算术函数上的卷积，这些卷积在Narkiewicz的意义上是正则的，在Burnett等人意义上是齐次的，并且是有界的，即存在一个共同的有限界来限制原始数的秩。 在这类“贪婪卷积”中，单位卷积和“三元卷积”特别有趣：它们是唯一的正则、齐次卷积，其中每个原始数具有相同的有限秩。 虽然长度为3的贪婪卷积也有秩为3和秩为1的原始数，并且详细描述了这一点，但它仍然很特殊，因为可以通过一种我们称为选择性筛选的简单递归过程生成原始数集合。 显示英文摘要

摘要： We introduce a class of convolutions on arithmetical functions that are regular in the sense of of Narkiewicz, homogeneous in the sense of Burnett et al, and bounded, in the sense that there exists a common finite bound for the rank of primitive numbers. Among these "greedy convolutions" the unitary convolution and the "ternary convolution" are particularly interesting: they are the only regular, homogeneous convolutions where each primitive number have the same finite rank. While the greedy convolution of length 3, also described in detail, has primitive numbers of rank 3 and rank 1, it is still special in that the set of primitives can be generated by a simple recursive procedure that we name selective sifting.