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Mathematics

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University of Central Florida

2015

Algebraic applications to tiling

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Tiling With Polyominoes, Polycubes, And Rectangles, Michael Saxton Jan 2015

Tiling With Polyominoes, Polycubes, And Rectangles, Michael Saxton

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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.