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

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

2007-06-22

arxiv.org/abs/0706.3218v2

Mathematics

Group Theory

28 pages, 13 figures

Scientific paper

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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