Alphabeta MathGarside Structure, Normal Forms, and the Center — Examples
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The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
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✓ 4 results · all verified · 0 also independently AI-judged
Every result on this page is machine-checked by a proof checker and read in full and owner-audited; the judge is an additional, independent cross-model AI review of the proofs. The 4 not AI-judged were verified by owner audit (typically over a confirmed judge false positive), not failures.
1 · Prerequisites
Abstract Algebra
Braid Groups
Category Theory
Coxeter Groups
Real Analysis
2 · Logical flowchart
3 · Items
Example
The simple braids and divisibility lattice for b three
Example
A left garside normal form computation in b three
Example
The full twist in b three
Counterexample
Exponent sum is not a complete braid normal form
Sources
- J. Gonzalez-Meneses, Basic results on braid groups, Section 4, printed pp. 26-29
- J. Birman and T. Brendle, Braids: A Survey, Section 5.1
- J. Gonzalez-Meneses, Basic results on braid groups, Section 4.1, printed pp. 29-30
- J. Gonzalez-Meneses, Basic results on braid groups, Theorem 4.2, printed pp. 30-31
- J. Birman and T. Brendle, Braids: A Survey, Section 5.2