Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$

IF 1 3区数学 Q1 MATHEMATICS Discrete Analysis Pub Date : 2018-05-29 DOI:10.19086/da.10570

Ruxi Shi

引用次数: 10

Abstract

We prove that on cyclic groups of square-free order, a tile is a spectral set. Moreover, we prove that the converse also holds on cyclic groups $\mathbb{Z}_{pqr}$ with $p,q,r$ distinct primes, that is to say, a spectral set is also a tile. As a consequence, Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$.

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Fuglede关于循环群$\mathbb的猜想成立{Z}_｛pqr｝$

证明了在无平方阶的循环群上，图是谱集。此外，我们证明了对于具有$p,q,r$不同素数的循环群$\mathbb{Z}_{pqr}$，逆命题也成立，即谱集也是块。因此，Fuglede的猜想在循环群$\mathbb{Z}_{pqr}$上成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Analysis Mathematics-Algebra and Number Theory

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

17 weeks

期刊介绍： Discrete Analysis is a mathematical journal that aims to publish articles that are analytical in flavour but that also have an impact on the study of discrete structures. The areas covered include (all or parts of) harmonic analysis, ergodic theory, topological dynamics, growth in groups, analytic number theory, additive combinatorics, combinatorial number theory, extremal and probabilistic combinatorics, combinatorial geometry, convexity, metric geometry, and theoretical computer science. As a rough guideline, we are looking for papers that are likely to be of genuine interest to the editors of the journal.

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