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.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Schofield, Jennifer L., "Growth and Geodesics of Thompson's Group F" (2009). Theses and Dissertations. 1977.
Thompson's group F, growth function, reduced pairs of trees, pipe systems