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Tiling with Polyominoes, Polycubes, and Rectangles

In this paper we study the hierarchical structure of the 2-d polyominoes. We introduce a new infinite family of polyominoes which we prove tiles a strip. We discuss applications of algebra to tiling. We discuss the algorithmic decidability of tiling the infinite plane Z x Z given a finite set of polyominoes. We will then discuss tiling with rectangles. We will then get some new, and some analogous results concerning the possible hierarchical structure for the 3-d polycubes.

Identiferoai:union.ndltd.org:ucf.edu/oai:stars.library.ucf.edu:etd-2437
Date01 January 2015
CreatorsSaxton, Michael
PublisherSTARS
Source SetsUniversity of Central Florida
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceElectronic Theses and Dissertations

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