Universal Upper Bound for the Growth of Artin Monoids

TL;DR

This paper establishes a universal upper bound of 4 for the growth rates of Artin monoids and links their generating functions to Chebyshev polynomials, with applications to Artin groups and braids.

Contribution

It proves a universal growth rate bound for Artin monoids and connects their generating functions to Chebyshev polynomials, offering new insights into their structure.

Findings

Growth rate upper bound of 4 for Artin monoids

Generating functions expressed via Chebyshev polynomials

Applications to Artin groups and positive braids

Abstract

In this paper we study the growth rates of Artin monoids and we show that 4 is a universal upper bound. We also show that the generating functions of the associated right-angled Artin monoids are given by families of Chebyshev polynomials. Applications to Artin groups and positive braids are given.