Alladi Ramakrishnan Hall

Length Generating Functions for Right-Angled Groups and Monoids

Amritanshu Prasad

IMSc

A right angled monoid is one whose generators are indexed by the nodes of a finite graph; generators whose nodes are joined by an edge are deemed to commute. The corresponding group is known as a right-angled Artin group. When the generators are made to be involutions, the resulting group is called a right-angled Coxeter group.

The length generating function for any of these objects is the generating function of the sequence c(n), where c(n) denotes the number of elements of length n. We show that this generating function is rational and explain how it can be computed by counting cliques in the graph.