Keywords

Tiling, cyclotomic, tijdeman

Abstract

A set tiles the integers if and only if the integers can be written as a disjoint union of translates of that set. Counterexamples based on finite Abelian groups show that Fuglede conjecture is false in high dimensions. A solution for the Fuglede conjecture in Z or all the groups ZN would provide a solution for the Fuglede conjecture in R. Focusing on tiles in dimension one, we will concentrate on the analysis of tiles in the finite groups ZN. Based on the Coven- Meyerowitz conjecture, it has been proved that if any spectral set in Z satisfies the the Coven-Meyerowitz properties, then every spectral set in R is a tile. We will present some of the main results related to integer tiles and give a self-contained description of the theory with detailed proofs.

Notes

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Graduation Date

2014

Semester

Spring

Advisor

Dutkay, Dorin

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematical Science; Industrial Mathematics

Format

application/pdf

Identifier

CFE0005199

URL

http://purl.fcla.edu/fcla/etd/CFE0005199

Language

English

Release Date

May 2014

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

Subjects

Dissertations, Academic -- Sciences; Sciences -- Dissertations, Academic

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Included in

Mathematics Commons

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