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). All Theses and Dissertations. 1977.
Thompson's group F, growth function, reduced pairs of trees, pipe systems