Keywords

Tiling, discrete, polyominoes, algebraic applications to tiling, rectangles, decidability

Abstract

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.

Notes

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Graduation Date

2015

Semester

Fall

Advisor

Reid, Michael

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematical Science

Format

application/pdf

Identifier

CFE0005995

URL

http://purl.fcla.edu/fcla/etd/CFE0005995

Language

English

Release Date

December 2015

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

Subjects

Dissertations, Academic -- Sciences; Sciences -- Dissertations, Academic

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Included in

Mathematics Commons

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