Thompson's Group F

Understand

We introduce forest diagrams and strand diagrams for elements of Thompson's group F.

• A forest diagram is a pair of infinite, bounded binary forests together with an order-preserving bijection of the leaves.
• Using forest diagrams, we derive a simple length formula for elements of F, and we discuss applications to the geometry of the Cayley graph, including a new upper bound on the isoperimetric constant (a.k.a.
• Cheeger constant) of F.