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The word problem for finite-rank Artin groups

Corollary 1.3 of the parabolic-intersections manuscript: there is an algorithm that, given a finite Coxeter matrix MM, a subset XX and words u,vu,v, decides whether v∈uAXu−1v\in uA_Xu^{-1}; with X=∅X=\varnothing this decides the word problem for every finite-rank Artin group. The algorithm uses the framed zigzag-algebra action, shown faithful in Section 8, computed exactly over a cyclotomic field, and tests one transported projective by Gaussian elimination. No complexity bound is asserted, and the conjugacy problem is not treated.

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Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The word problem for finite-rank Artin groups · Word problem for Artin groups

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Unreleased internal OpenAI model
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Lineage and corrections

Charney, Problems related to Artin groups (Problem 1) evidence for this event

This event attributed to Unreleased internal OpenAI model

Blasco-Garcia et al. 2026, Rewriting in Artin groups without A3 or B3 subdiagrams evidence for this event

Parabolic intersections in Artin groups (companion, same harmonic-height method) evidence for this event

Corollary 1.3 of the parabolic-intersections manuscript: there is an algorithm that, given a finite Coxeter matrix MM, a subset XX and words u,vu,v, decides whether v∈uAXu−1v\in uA_Xu^{-1}; with X=∅X=\varnothing this decides the word problem for every finite-rank Artin group. The algorithm uses the framed zigzag-algebra action, shown faithful in Section 8, computed exactly over a cyclotomic field, and tests one transported projective by Gaussian elimination. No complexity bound is asserted, and the conjugacy problem is not treated. parent of this event

VibeMathed record: The word problem for finite-rank Artin groups evidence for this event

The word problem for finite-rank Artin groups parent of this event

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