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Record W4385585618 · doi:10.26493/1855-3974.2835.8f0

On the minisymposium problem

2023· article· en· W4385585618 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

VenueArs Mathematica Contemporanea · 2023
Typearticle
Languageen
FieldEngineering
Topicgraph theory and CDMA systems
Canadian institutionsCarleton UniversityUniversity of TorontoToronto Metropolitan University
FundersNatural Sciences and Engineering Research Council of CanadaGruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni
KeywordsCombinatoricsMathematicsContext (archaeology)FactorizationGraphDiscrete mathematicsAlgorithm

Abstract

fetched live from OpenAlex

The generalized Oberwolfach problem asks for a factorization of the complete graph Kv into prescribed 2-factors and at most a 1-factor. When all 2-factors are pairwise isomorphic and v is odd, we have the classic Oberwolfach problem, which was originally stated as a seating problem: given v attendees at a conference with t circular tables such that the ith table seats ai people and ∑t{i=1} ai = v, find a seating arrangement over the (v-1)/2 days of the conference, so that every person sits next to each other person exactly once. In this paper we introduce the related minisymposium problem, which requires a solution to the generalized Oberwolfach problem on v vertices that contains a subsystem on m vertices. That is, the decomposition restricted to the required m vertices is a solution to the generalized Oberwolfach problem on m vertices. In the seating context above, the larger conference contains a minisymposium of m participants, and we also require that pairs of these m participants be seated next to each other for ⌊(m−1)/2⌋ of the days. When the cycles are as long as possible, i.e. v, m and v − m, a flexible method of Hilton and Johnson provides a solution. We use this result to provide further solutions when v ≡ m ≡ 2 (mod 4) and all cycle lengths are even. In addition, we provide extensive results in the case where all cycle lengths are equal to k, solving all cases when m ∣ v, except possibly when k is odd and v is even.

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 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 score0.409
Threshold uncertainty score0.998

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)0.0000.003

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 head0.018
GPT teacher head0.204
Teacher spread0.186 · 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