COMPUTING WORD LENGTH IN ALTERNATE PRESENTATIONS OF THOMPSON'S GROUP F

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 Xn = {x0,x1, …,xn}, which is a subset of the standard infinite generating set for F. We use this method to show that (F, Xn) is not almost convex, and has pockets of increasing, though bounded, depth dependent on n.