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Record W2963698649

A relation between clar covering polynomial and cube polynomial

2013· article· en· W2963698649 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.

Bibliographic record

VenueLanzhou University Institutional Repository · 2013
Typearticle
Languageen
FieldMathematics
TopicGraph theory and applications
Canadian institutionsToronto Metropolitan University
Fundersnot available
KeywordsBijectionPolynomialCombinatoricsCube (algebra)Tutte polynomialHypercubeHexagonal crystal systemMathematicsZhàngGraphRelation (database)Computer scienceChemistryCrystallographyMathematical analysisGeography
DOInot available

Abstract

fetched live from OpenAlex

The Clar covering polynomial (Zhang-Zhang polynomial) of a hexagonal system is a counting polynomial of resonant structures called Clar covers, which can be used to determine the Kekule count, the first Herndon number and Clar number. In this paper we prove that the Clar covering polynomial of a hexagonal system H coincides with the cube polynomial of its resonance graph R(H) by establishing a bijection between the Clar covers of H and the hypercubes in R(H). Moreover, some important applications of this relation are presented.

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)0.000
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: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.816
Threshold uncertainty score0.550

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0010.000
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 head0.019
GPT teacher head0.222
Teacher spread0.203 · 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