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Record W92501153 · doi:10.37236/12156

Computation in Coxeter Groups—I. Multiplication

2002· article· en· W92501153 on OpenAlexaff
Bill Casselman

Bibliographic record

VenueThe Electronic Journal of Combinatorics · 2002
Typearticle
Languageen
FieldComputer Science
Topicsemigroups and automata theory
Canadian institutionsUniversity of British Columbia
Fundersnot available
KeywordsCoxeter groupMathematicsCoxeter elementArtin groupCoxeter complexMultiplication (music)ComputationMathematical proofReflection (computer programming)CombinatoricsAlgebra over a fieldAlgorithmPure mathematicsComputer scienceGeometryProgramming language

Abstract

fetched live from OpenAlex

An efficient and purely combinatorial algorithm for calculating products in arbitrary Coxeter groups is presented, which combines ideas of Fokko du Cloux and myself. Proofs are largely based on geometry. The algorithm has been implemented in practical Java programs, and runs surprisingly quickly. It seems to be good enough in many interesting cases to build the minimal root reflection table of Brink and Howlett, which can be used for a more efficient multiplication routine.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.653
Threshold uncertainty score0.257

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.010
GPT teacher head0.219
Teacher spread0.209 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one teacher head, not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations14
Published2002
Admission routes1
Has abstractyes

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