Growth and Geodesics of Thompson's Group F

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...

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Main Author:	Schofield, Jennifer L.
Format:	Others
Published:	BYU ScholarsArchive 2009
Subjects:	Thompson's group F growth function reduced pairs of trees pipe systems Mathematics
Online Access:	https://scholarsarchive.byu.edu/etd/1977 https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2976&context=etd

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spelling	ndltd-BGMYU2-oai-scholarsarchive.byu.edu-etd-29762021-09-01T05:01:40Z Growth and Geodesics of Thompson's Group F Schofield, Jennifer L. 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. 2009-11-19T08:00:00Z text application/pdf https://scholarsarchive.byu.edu/etd/1977 https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2976&context=etd http://lib.byu.edu/about/copyright/ Theses and Dissertations BYU ScholarsArchive Thompson's group F growth function reduced pairs of trees pipe systems Mathematics
collection	NDLTD
format	Others
sources	NDLTD
topic	Thompson's group F growth function reduced pairs of trees pipe systems Mathematics
spellingShingle	Thompson's group F growth function reduced pairs of trees pipe systems Mathematics Schofield, Jennifer L. Growth and Geodesics of Thompson's Group F
description	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.
author	Schofield, Jennifer L.
author_facet	Schofield, Jennifer L.
author_sort	Schofield, Jennifer L.
title	Growth and Geodesics of Thompson's Group F
title_short	Growth and Geodesics of Thompson's Group F
title_full	Growth and Geodesics of Thompson's Group F
title_fullStr	Growth and Geodesics of Thompson's Group F
title_full_unstemmed	Growth and Geodesics of Thompson's Group F
title_sort	growth and geodesics of thompson's group f
publisher	BYU ScholarsArchive
publishDate	2009
url	https://scholarsarchive.byu.edu/etd/1977 https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2976&context=etd
work_keys_str_mv	AT schofieldjenniferl growthandgeodesicsofthompsonsgroupf
_version_	1719473275373879296

Growth and Geodesics of Thompson's Group F

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