Rewriting systems and orderability of Artin monoids
by
Patrick Bahls
University of Illinois, Urbana-Champaign
Coauthors: Tyler Smith (University of Illinois, Urbana-Champaign)

Let (A, S) be a large-type Artin system. We adapt a method of S. Burckel to define a linear order on the elements of A by considering an order on rooted, labeled trees. In order to show that this order is invariant with respect to multiplication on the left, we make use of a normal form for A and a confluent and terminating rewriting system which produces the normal form of a given element.

The main theorem generalizes earlier results regarding finite-type and right-angled Artin groups.

Date received: February 17, 2005