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

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

Codex  0 Created 2026-09-24 Updated 2026-09-25

m_{ij} < \infty

, the braid relation in a Coxeter group is

m_{ij} factors s_{i} s_{j} s_{i} \dots = m_{ij} factors s_{j} s_{i} s_{j} \dots .

(1)

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.

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