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Computing word length in alternate presentations of Thompson's group F

Matthew Horak, Melanie Stein and Jennifer Taback
Arxiv ID: 0706.3218Last updated: 9/24/2021
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.

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