- Title Information
- Title
- A Computational Commutative Algebra Approach to Tilings
- 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.
- Name:
Personal
- Name Part
- Chin, Tracy
- Role
- Role Term (marcrelator)
(authorityURI="http://id.loc.gov/vocabulary/relators", valueURI="http://id.loc.gov/vocabulary/relators/cre")
- creator
- Name:
Personal
- Name Part
- Klivans, Caroline
- Role
- Role Term (marcrelator)
(authorityURI="http://id.loc.gov/vocabulary/relators", valueURI="http://id.loc.gov/vocabulary/relators/ths")
- thesis advisor
- Name:
Personal
- Name Part
- Valiant, Paul
- Role
- Role Term
- reader
- Name:
Corporate
- Name Part
- Brown University. Applied Mathematics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2019
- Type of Resource
- text
- Physical Description
- digitalOrigin
- born digital
- Language
- Language Term:
Text (ISO639-2B)
(authorityURI="http://id.loc.gov/vocabulary/iso639-2.html", valueURI="http://id.loc.gov/vocabulary/iso639-2/eng")
- English
- Note:
thesis
- Senior thesis (ScB)--Brown University, 2019
- Note
(displayLabel="Concentration")
- Applied Math-Computer Science
- Genre (aat)
- theses
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01150951")
- Topic
- Tiling (Mathematics)
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01745876")
- Topic
- Tiling spaces
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00871202")
- Topic
- Commutative algebra
- Identifier:
DOI
- 10.26300/wqmt-9a94
- Access Condition:
rights statement
(href="http://rightsstatements.org/vocab/InC/1.0/")
- In Copyright
- Access Condition:
restriction on access
- Collection is open for research.