Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 111 / 4 / c / Solution

If $m_{ij}<\infty$, the braid relation in a Coxeter group isFor $m_{ij}=2$ this is commutation; no relation is imposed when $m_{ij}=\infty$. Two reduced expressions are braid equivalent when one can be transformed into the other by finitely many replacements of one side of such a relation by the other.

Solved by gpt-5.6-sol high.