Artin groups of large type are shortlex automatic with regular geodesics

TL;DR

This paper proves that Artin groups of large type are shortlex automatic with regular geodesic words, establishing important properties for their computational and algebraic structure.

Contribution

It demonstrates that all large type Artin groups are shortlex automatic and have regular geodesic languages satisfying the Falsification by Fellow-Traveller Property.

Findings

Artin groups of large type are shortlex automatic.

The set of geodesic words is regular.

Geodesic words satisfy the Falsification by Fellow-Traveller Property.

Abstract

We prove that any Artin group of large type is shortlex automatic with respect to its standard generating set, and that the set of all geodesic words over the same generating set satisfies the Falsification by Fellow-Traveller Property (FFTP) and hence is regular.