Forest diagrams for elements of Thompson's group F

Abstract

We introduce forest diagrams to represent elements of Thompson's group F. These diagrams relate to a certain action of F on the real line in the same way that tree diagrams relate to the standard action of F on the unit interval. Using forest diagrams, we give a conceptually simple length formula for elements of F with respect to the {x_0,x_1} generating set, and we discuss the construction of minimum-length words for positive elements. Finally, we use forest diagrams and the length formula to examine the structure of the Cayley graph of F.

44 pages, 70 figures

Cited by in corpus (6)

• Some geodesic problems in groups
• A computational approach to the Thompson group $F$
• Counting elements and geodesics in Thompson's group $F$
• Cone types and geodesic languages for lamplighter groups and Thompson's group F
• Interprétation de l'Arithmétique dans certains groupes de permutations affines par morceaux d'un intervalle
• Computing word length in alternate presentations of Thompson's group F