Date of Award
2007
Document Type
Thesis
Publication Status
Version of Record
Submission Date
October 2026
Thesis/Dissertation Advisor [Chair]
Meyerowitz, Aaron
Abstract
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.
Extent
40 p.
Recommended Citation
Cattell, Liam J., "Tiling Z with Triples Using Signed Permutation Matrices" (2007). Electronic Theses and Dissertations 2000 - 2009. 1384.
https://digitalcommons.fau.edu/etd_general_5/1384
Identifier
FA00000732
Comments
Includes bibliography.|Thesis (M.S.)--Florida Atlantic University, 2007.|Charles E. Schmidt College of Science|FAU Electronic Theses and Dissertations Collection|Includes bibliography.