Tiling, cyclotomic, tijdeman
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.
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Master of Science (M.S.)
College of Sciences
Mathematical Science; Industrial Mathematics
Length of Campus-only Access
Masters Thesis (Open Access)
Dissertations, Academic -- Sciences; Sciences -- Dissertations, Academic
Li, Shasha, "Tiling the Integers" (2014). Electronic Theses and Dissertations, 2004-2019. 4709.