Description
- Abstract:
- In 1990, Thurston proved that for any two-dimensional simply connected region, the space of tilings is flip-connected. Later, Yamzon reproved this result using a commutative algebra approach developed by Gross. In the first portion of this thesis, we further explore the algebraic structures from Gross and Yamzon's work. Specifically, we prove a primary decomposition of the flip ideal for small (3 x n) regions, and give a conjecture for the primary decomposition in larger regions. In the second portion of the thesis, we give preliminary computational results on the flip-connected components of three-dimensional tilings.
- Notes:
- Senior thesis (ScB)--Brown University, 2019
- Concentration: Applied Math-Computer Science
Access Conditions
- Rights
- In Copyright
- Restrictions on Use
- Collection is open for research.
Citation
Chin, Tracy,
"A Computational Commutative Algebra Approach to Tilings"
(2019).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.26300/wqmt-9a94
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Applied Mathematics Theses and Dissertations
Theses and Dissertations for the Applied Mathematics department....