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.

Author dc:creator

• Saxton, Michael

Contributors dc:contributor

• Reid, Michael

• Tiling
• discrete
• polyominoes
• algebraic applications to tiling
• rectangles
• decidability
• Mathematics
• Dissertations, Academic -- Sciences; Sciences -- Dissertations, Academic

Language dc:language

English

Identifier

CFE0005995

OAI identifier oai:identifier

oai:stars.library.ucf.edu:etd-2437