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Record W2043757383 · doi:10.4153/cmb-2007-050-x

Asymptotic Existence of Resolvable Graph Designs

2007· article· en· W2043757383 on OpenAlex
Peter J. Dukes, Alan C. H. Ling

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.
venuePublished in a venue whose home country is Canada.

Bibliographic record

VenueCanadian Mathematical Bulletin · 2007
Typearticle
Languageen
FieldEngineering
Topicgraph theory and CDMA systems
Canadian institutionsUniversity of Victoria
FundersArmy Research OfficeDeutscher Akademischer Austauschdienst
KeywordsMathematicsCombinatoricsPartition (number theory)GraphVertex (graph theory)Simple graphDiscrete mathematics

Abstract

fetched live from OpenAlex

Abstract Let v ≥ k ≥ 1 and λ ≥ 0 be integers. A block design BD( v , k , λ) is a collection of k -subsets of a v -set X in which every unordered pair of elements from X is contained in exactly λ elements of . More generally, for a fixed simple graph G , a graph design GD( v , G , λ) is a collection of graphs isomorphic to G with vertices in X such that every unordered pair of elements from X is an edge of exactly λ elements of . A famous result of Wilson says that for a fixed G and λ, there exists a GD( v , G , λ) for all sufficiently large v satisfying certain necessary conditions. A block (graph) design as above is resolvable if can be partitioned into partitions of (graphs whose vertex sets partition) X . Lu has shown asymptotic existence in v of resolvable BD( v , k , λ), yet for over twenty years the analogous problem for resolvable GD( v , G , λ) has remained open. In this paper, we settle asymptotic existence of resolvable graph designs.

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 categoriesInsufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
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 score0.490
Threshold uncertainty score0.999

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)0.0030.002

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 head0.015
GPT teacher head0.197
Teacher spread0.182 · 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