The density of tuples restricted by relatively r-prime conditions

Sittinger, Brian D. and Chen, Vickie V. (2024) The density of tuples restricted by relatively r-prime conditions. Miskolc Mathematical Notes, 25 (1). pp. 465-477. ISSN 1787-2413

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Abstract

In order to consider j-wise relative r-primality conditions that do not necessarily require all j-tuples of elements in a Dedekind domain to be relatively r-prime, we define the notion of j-wise relative r-primality with respect to a fixed j-uniform hypergraph H. This allows us to provide further generalisations to several results on natural densities not only for a ring of algebraic integers O, but also for the ring F_q[x].

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