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Record W1598186826 · doi:10.37236/1548

Small Forbidden Configurations II

2000· article· en· W1598186826 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueThe Electronic Journal of Combinatorics · 2000
Typearticle
Languageen
FieldEngineering
Topicgraph theory and CDMA systems
Canadian institutionsUniversity of British Columbia
FundersNatural Sciences and Engineering Research Council of CanadaUniversity of British Columbia
KeywordsCombinatoricsMathematicsNotationPermutation (music)Vertex (graph theory)Matrix (chemical analysis)Discrete mathematicsGraphPhysicsArithmetic

Abstract

fetched live from OpenAlex

The present paper continues the work begun by Anstee, Griggs and Sali on small forbidden configurations. In the notation of (0,1)-matrices, we consider a (0,1)-matrix $F$ (the forbidden configuration), an $m\times n$ (0,1)-matrix $A$ with no repeated columns which has no submatrix which is a row and column permutation of $F$, and seek bounds on $n$ in terms of $m$ and $F$. We give new exact bounds for some $2\times l$ forbidden configurations and some asymptotically exact bounds for some other $2\times l$ forbidden configurations. We frequently employ graph theory and in one case develop a new vertex ordering for directed graphs that generalizes Rédei's Theorem for Tournaments. One can now imagine that exact bounds could be available for all $2\times l$ forbidden configurations. Some progress is reported for $3\times l$ forbidden configurations. These bounds are improvements of the general bounds obtained by Sauer, Perles and Shelah, Vapnik and Chervonenkis.

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.

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: Empirical
Teacher disagreement score0.127
Threshold uncertainty score0.285

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
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 head0.007
GPT teacher head0.175
Teacher spread0.169 · 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