Computing word length in alternate presentations of Thompson's group F
Group Theory
2021-09-24 v2
Abstract
We introduce a new method for computing the word length of an element of Thompson's group F with respect to a "consecutive" generating set of the form X_n={x_0,x_1,...,x_n}, which is a subset of the standard infinite generating set for F. We use this method to show that (F,X_n) is not almost convex, and has pockets of increasing, though bounded, depth dependent on n.
Cite
@article{arxiv.0706.3218,
title = {Computing word length in alternate presentations of Thompson's group F},
author = {Matthew Horak and Melanie Stein and Jennifer Taback},
journal= {arXiv preprint arXiv:0706.3218},
year = {2021}
}
Comments
28 pages, 13 figures