Abstract
In this Independent Study, we survey the mathematics of tiling 2-dimensional regions with polyomino shapes of varying sizes. We investigate tile invariants to prove tileability and examine specific tile invariants, such as the Conway/Lagarias invariant. Using "Tile Invariants for Tackling Tiling Questions" by Dr. Michael Hitchman as a guide for exploration, we survey different techniques for finding tile invariants, such as coloring, boundary words, height, and group theoretic techniques. After this background is established, we answer an open problem posed by Hitchman in the affirmative - we prove the requirements for a modified rectangle to be tileable by area 5 ribbon tiles. In the final part of this project, we consider L-pentominoes and conjecture the requirements for a rectangle to be tileable by this tile set. We prove the conjecture in certain cases.
Advisor
Chowdhury, Subhadip
Department
Mathematics
Recommended Citation
Wickham, Lucy, "Tile Invariants and an Exploration of Tilings with Ribbon Pentominoes and L-Pentominoes" (2023). Senior Independent Study Theses. Paper 10761.
https://openworks.wooster.edu/independentstudy/10761
Disciplines
Discrete Mathematics and Combinatorics | Other Mathematics
Keywords
tiling, tile invariants, ribbon tiles, pentominoes
Publication Date
2023
Degree Granted
Bachelor of Arts
Document Type
Senior Independent Study Thesis
© Copyright 2023 Lucy Wickham