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Record W282701158

The Actions of Fractional Automorphisms

2004· article· en· W282701158 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.

venuePublished in a venue whose home country is Canada.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueJournal of Combinatorial Mathematics and Combinatorial Computing · 2004
Typearticle
Languageen
FieldMathematics
TopicGraph theory and applications
Canadian institutionsnot available
Fundersnot available
KeywordsMathematicsAutomorphismAdjacency matrixCombinatoricsVertex (graph theory)Permutation matrixIsomorphism (crystallography)Discrete mathematicsGraphCirculant matrix
DOInot available

Abstract

fetched live from OpenAlex

AbstractA fractional automorphism of a graph is a doubly stochastic ma-trix which commutes with the adjacency matrix of the graph. If weapply an ordinary automorphism to a set of vertices with a particularproperty, such as being independent or dominating, the resulting setretains that property. We examine the circumstances under whichfractional automorphisms preserve the fractional properties of func-tions on the vertex set. 1 Introduction In [6] a fractional isomorphism between two graphs with adjacency matricesA,B is defined to be a doubly stochastic matrix S with the property thatAS = SB. This definition is found by generalising the view of ordinarygraph isomorphisms as permutation matrices. It is natural to consider thecase when A = B; any doubly-stochastic matrix S such that SA = AS canbe considered a fractional automorphism. It is understood that a matrix hasthe property of being a fractional automorphism (or isomorphism) subjectto a certain ordering of the vertices, imposed by the ordering used in theadjacency matrix.Fractional automorphisms have been studied, though not under thatname, by Tinhofer in [4, 5] and Godsil in [2]. It is obvious that the set ofall fractional automorphisms of a graph with adjacency matrix A, which weshall denote by S(A), contains the convex hull of the set of automorphismstaken as permutation matrices; a graph is called compact if these two setsare in fact equal. While several classes of graphs are known to be compact,as yet no good characterisation of compact graphs has been found.

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)0.002
metaresearch head score (Gemma)0.001
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 score0.024
Threshold uncertainty score0.561

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.001
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 head0.029
GPT teacher head0.300
Teacher spread0.271 · 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