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Record W2501921681 · doi:10.1017/s0025557200184165

Integral powers of order three Latin square matrices

2009· article· en· W2501921681 on OpenAlexaff
Nicolas Gauthier

Bibliographic record

VenueThe Mathematical Gazette · 2009
Typearticle
Languageen
FieldEngineering
Topicgraph theory and CDMA systems
Canadian institutionsRoyal Military College of CanadaRoyal Ottawa Mental Health Centre
Fundersnot available
KeywordsLatin squarePermutation (music)Permutation matrixMathematicsMatrix (chemical analysis)Square matrixPermutation groupOrder (exchange)CombinatoricsEuler's formulaGroup (periodic table)Set (abstract data type)Algebra over a fieldPure mathematicsComputer scienceSymmetric matrixPhysicsMathematical analysis

Abstract

fetched live from OpenAlex

An order-n Latin square contains numbers, each of which is one of a set of n real numbers, , arranged in the form of an n × n matrix, in such a way that each row and each column of the matrix contains all n numbers. Euler (1707-1783) was the first to study the properties of Latin squares and they have been the focus of continued attention since. Studies of Latin squares naturally lead one to elements of group theory and of matrix theory. As will be shown in this note, both of these features may offer interesting investigative opportunities for classroom discussions of the permutation group on three symbols and of the algebra of the associated permutation matrices.

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 machine prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.003
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.015
Threshold uncertainty score0.050

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.003
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.001
Science and technology studies0.0010.003
Scholarly communication0.0020.002
Open science0.0000.001
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0150.002

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 head0.210
Teacher spread0.201 · 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 source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designNot applicable
Domainnot available
GenreOther

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

Citations1
Published2009
Admission routes1
Has abstractyes

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