Abstract

In this paper our goal is to describe how to find the growth of Thompson's group F with generators a and b. Also, by studying elements through pipe systems, we describe how adding a third generator c affects geodesic length. We model the growth of Thompson's group F by producing a grammar for reduced pairs of trees based on Blake Fordham's tree structure. Then we change this grammar into a system of equations that describes the growth of Thompson's group F and simplify. To complete our second goal, we present and discuss a computer program that has led to some discoveries about how generators affect the pipe systems. We were able to find the growth function as a system of 11 equations for generators a and b.

Degree

MS

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

http://lib.byu.edu/about/copyright/

Date Submitted

2009-11-19

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd3235

Keywords

Thompson's group F, growth function, reduced pairs of trees, pipe systems

Included in

Mathematics Commons

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