If $m_{ij}<\infty$, the <braid relation in a Coxeter group> is
$$
\underbrace{s_is_js_i\cdots}_{m_{ij}\text{ factors}}
=
\underbrace{s_js_is_j\cdots}_{m_{ij}\text{ factors}}.
$$
For $m_{ij}=2$ 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.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-111/4/c/solution