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Tiling Z with Triples Using Signed Permutation Matrices
 Date Issued:
 2007
 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 3subsets 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.
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 

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 3subsets 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 

Subject(s): 
Tiling (Mathematics) Sequences (Mathematics) Permutation groups 

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Host Institution:  FAU  
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