On the rank of Coxeter groups

TL;DR

This paper proves that for Coxeter groups with sufficiently large non-diagonal entries in their Coxeter matrix, the standard generating set is minimal in size, highlighting a condition for minimal generating sets.

Contribution

It establishes a new criterion linking the size of Coxeter matrix entries to the minimality of the standard generating set.

Findings

Standard generating set is minimal for large matrix entries.

Provides a condition for minimality based on Coxeter matrix entries.

Enhances understanding of Coxeter group structure.

Abstract

We show that the standard generating set of a Coxeter group is of minimal cardinality provided that the non-diagonal entries of the Coxeter matrix are sufficiently large.