Forest diagrams for elements of Thompson's group F
Group Theory
2018-10-30 v1
Abstract
We introduce forest diagrams to represent elements of Thompson's group F. These diagrams relate to a certain action of F on the real line in the same way that tree diagrams relate to the standard action of F on the unit interval. Using forest diagrams, we give a conceptually simple length formula for elements of F with respect to the {x_0,x_1} generating set, and we discuss the construction of minimum-length words for positive elements. Finally, we use forest diagrams and the length formula to examine the structure of the Cayley graph of F.
Keywords
Cite
@article{arxiv.math/0305412,
title = {Forest diagrams for elements of Thompson's group F},
author = {James M. Belk and Kenneth S. Brown},
journal= {arXiv preprint arXiv:math/0305412},
year = {2018}
}
Comments
44 pages, 70 figures