Date of Submission
Spring 2013
Academic Program
Computer Science; Mathematics
Project Advisor 1
James Belk
Project Advisor 2
Robert McGrail
Abstract/Artist's Statement
In this project, we present an efficient implementation of the solution to the conjugacy problem in Thompson's group F, a certain infinite group whose elements are piecewise-linear homeomorphisms of the unit interval [0; 1]. Our algorithm checks for conjugacy by constructing and comparing directed graphs called strand diagrams. We provide a comprehensive description of our solution algorithm, including the data structure we used to hold strand diagrams and the additional subroutines for manipulations of strand diagrams. We prove that our algorithm theoretically achieves an O(n) bound in the size of the input, and we present a O(n2) working solution as an executable JAR file, a web application, and Java source code.
Distribution Options
Access restricted to On-Campus only
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Recommended Citation
Hossain, Nabil Tarique, "Implementation of the Solution to the Conjugacy Problem in Thompson's Groups" (2013). Senior Projects Spring 2013. 45.
https://digitalcommons.bard.edu/senproj_s2013/45
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