On finite unions of ideals and cosets

Abstract

Although it is well known that the growth of Thompson's group F is exponential, the exact growth function is still unknown. Elements of its submonoid of positive words can be described using a binary rooted tree, whose norm can be computed assigning weights to each caret. Combining this fact with a combinatorial argument, the growth function of the submonoid is computed and thus providing a first step in the computation of the growth function of the group, as well as a lower bound for the growth rate for the group.