# Asymptotic combinatorics of Artin-Tits monoids and of some other monoids

## TL;DR

This paper develops methods to analyze the combinatorial structure of large random elements in Artin-Tits monoids, with broader applicability to other monoids like dual braid monoids, enhancing understanding of their normal forms.

## Contribution

It introduces new combinatorial methods for studying the normal forms of large random elements in Artin-Tits monoids and extends these methods to a general axiomatic framework.

## Key findings

- Methods effectively analyze large random elements in Artin-Tits monoids
- Framework applies to other monoids such as dual braid monoids
- Advances understanding of monoid normal form combinatorics

## Abstract

We introduce methods to study the combinatorics of the normal form of large random elements in Artin-Tits monoids. These methods also apply in an axiomatic framework that encompasses other monoids such as dual braid monoids.