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Tiling Z with Triples Using Signed Permutation Matrices
| Title: | Tiling Z with Triples Using Signed Permutation Matrices. |
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| Name(s): |
Cattell, Liam J. Meyerowitz, Aaron, Thesis advisor Florida Atlantic University, Degree grantor |
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| Type of Resource: | text | |
| Genre: | Electronic Thesis Or Dissertation | |
| Date Created: | 2007 | |
| Date Issued: | 2007 | |
| Publisher: | Florida Atlantic University | |
| Place of Publication: | Boca Raton, Fla. | |
| Physical Form: | application/pdf | |
| Extent: | 40 p. | |
| Language(s): | English | |
| Summary: | The topic of this paper is tiling the integers with triples, or more precisely to write Z as a disjoint union of translates of a given set of 3-subsets composed of basic shapes called prototiles. We fix the set of proto tiles P = { { 0, a, a+ v} , { U. b, a+ b}} and define an algorithm which returns a sequence of translates of P when given an initial subset of Z representing integers that are already tiled. This algorithm is then adapted to describe all possible tilings with triples from P using the action of certain signed permutation matrices on a subset of za+b , uamdy the 2" Yectors with all entries ±1. Given b > 2a, we research properties of the digraph of all possible tiling states and some related digraphs. | |
| Identifier: | FA00000732 (IID) | |
| Collection: | FAU Electronic Theses and Dissertations Collection | |
| Note(s): |
Includes bibliography. Thesis (M.S.)--Florida Atlantic University, 2007. Charles E. Schmidt College of Science |
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| Subject(s): |
Tiling (Mathematics) Sequences (Mathematics) Permutation groups |
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| Held by: | Florida Atlantic University Libraries | |
| Persistent Link to This Record: | http://purl.flvc.org/fau/fd/FA00000732 | |
| Sublocation: | Digital Library | |
| Use and Reproduction: | Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. | |
| Use and Reproduction: | http://rightsstatements.org/vocab/InC/1.0/ | |
| Host Institution: | FAU | |
| Is Part of Series: | Florida Atlantic University Digital Library Collections. |
