Tiling, discrete, polyominoes, algebraic applications to tiling, rectangles, decidability
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.
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Master of Science (M.S.)
College of Sciences
Length of Campus-only Access
Masters Thesis (Open Access)
Dissertations, Academic -- Sciences; Sciences -- Dissertations, Academic
Saxton, Michael, "Tiling with Polyominoes, Polycubes, and Rectangles" (2015). Electronic Theses and Dissertations. 1438.