What the study found
The study found a polynomial isoperimetric function, n^6, for a class of Artin groups whose defining graph has no edges labelled by 3. The authors also state that this shows even Artin groups have a solvable word problem.
Why the authors say this matters
The authors conclude that the result shows even Artin groups have a solvable word problem. They present the finding as a consequence of the polynomial isoperimetric bound.
What the researchers tested
The researchers studied Artin groups with defining graphs that contain no edges labelled by 3. They used small cancellation theory of relative extended presentations to obtain an isoperimetric function.
What worked and what didn't
What worked was obtaining a polynomial isoperimetric function of n^6 for the stated class of Artin groups. The abstract does not describe any failed approach or comparison with other bounds.
What to keep in mind
The abstract only describes the class of Artin groups whose defining graph has no edges labelled by 3. It does not provide additional limitations, examples, or details of the proof beyond the use of small cancellation theory of relative extended presentations.
Key points
- A polynomial isoperimetric function n^6 was found for a class of Artin groups.
- The class considered consists of Artin groups whose defining graph has no edges labelled by 3.
- The authors say the result shows even Artin groups have a solvable word problem.
- The method used was small cancellation theory of relative extended presentations.
Disclosure
- Research title:
- Polynomial isoperimetric function found for a class of Artin groups
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