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Tiling with Polyominoes, Polycubes, and Rectangles

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Date Issued:
2015
Abstract/Description:
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.
Title: Tiling with Polyominoes, Polycubes, and Rectangles.
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Name(s): Saxton, Michael, Author
Reid, Michael, Committee Chair
Lee, Junho, Committee Member
Han, Deguang, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2015
Publisher: University of Central Florida
Language(s): English
Abstract/Description: 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.
Identifier: CFE0005995 (IID), ucf:50791 (fedora)
Note(s): 2015-12-01
M.S.
Sciences, Mathematics
Masters
This record was generated from author submitted information.
Subject(s): Tiling -- Discrete -- Polyominoes -- Algebraic Applications to Tiling -- Rectangles -- Decidability
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0005995
Restrictions on Access: public 2015-12-15
Host Institution: UCF

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