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Existence of large independent-like sets

Volume 159 / 2020

Robert (Xu) Yang Colloquium Mathematicum 159 (2020), 107-118 MSC: Primary 43A25; Secondary 43A46. DOI: 10.4064/cm7649-11-2018 Published online: 18 October 2019

Abstract

Let $G$ be a compact abelian group and $\varGamma $ be its discrete dual group. For $N \in \mathbb N $, we define a class of independent-like sets, $N$-PR sets, to be sets in $\Gamma $ such that every $\mathbb Z _N$-valued function defined on the set can be interpolated by a character in $G$.

These sets are examples of $\varepsilon $-Kronecker sets and Sidon sets. In this paper we study various properties of $N$-PR sets. We give a characterization of $N$-PR sets, describe their structure and prove the existence of large $N$-PR sets.

Authors

  • Robert (Xu) YangDepartment of Pure Mathematics
    University of Waterloo
    Waterloo, ON, Canada N2L 3G1
    e-mail

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