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Tiling the Integers
| Title: | Tiling the Integers. |
 52 views 24 downloads |
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| Name(s): |
Li, Shasha, Author Dutkay, Dorin, Committee Chair Han, Deguang, Committee Member Sun, Qiyu, Committee Member , Committee Member University of Central Florida, Degree Grantor |
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| Type of Resource: | text | |
| Date Issued: | 2014 | |
| Publisher: | University of Central Florida | |
| Language(s): | English | |
| Abstract/Description: | 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 ?nite Abelian groups show that Fuglede conjecture is false inhigh 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 ?nite groups ZN. Based on the Coven- Meyerowitz conjecture, it has been proved that if any spectral set in Z satis?es the the Coven-Meyerowitz properties, then everyspectral 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. | |
| Identifier: | CFE0005199 (IID), ucf:50642 (fedora) | |
| Note(s): |
2014-05-01 M.S. Sciences, Mathematics Masters This record was generated from author submitted information. |
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| Subject(s): | tiling -- cyclotomic -- Tijdeman | |
| Persistent Link to This Record: | http://purl.flvc.org/ucf/fd/CFE0005199 | |
| Restrictions on Access: | public 2014-05-15 | |
| Host Institution: | UCF |
