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Record W1530347015 · doi:10.1285/i15900932v21n1p1

An Eightfold Littlewood-Richardson Theorem

2013· article· it· W1530347015 on OpenAlex
Manfred Schocker

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

VenueUniversità del Salento · 2013
Typearticle
Languageit
FieldMathematics
TopicAdvanced Combinatorial Mathematics
Canadian institutionsUniversité du Québec à Montréal
Fundersnot available
KeywordsBijection, injection and surjectionBijectionMathematicsCombinatoricsInvariant (physics)SkewAlphabetSet (abstract data type)Generating functionDiscrete mathematicsComputer science

Abstract

fetched live from OpenAlex

Based on a generalized ordering on a set , Schensted's  insertion mapping is defined on the set of words over the ordered alphabet . In this general framework, a transparent approach to various versions of the Robinson-Schensted correspondence and of invariant properties originally due to Schutzenberger, Knuth, White e.a. is obtained.  Furthermore, eight combinatorial descriptions of the Littlewood-Richardson coefficients are obtained simultaneously, and direct bijections between the corresponding sets, including the bijection of Hanlon and Sundaram. Some of these descriptions may be translated into identities of skew Schur functions discovered by Aitken and Berenstein/Zelevinsky.

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 categoriesMeta-epidemiology (narrow), Insufficient 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 score0.144
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.002
Open science0.0010.000
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0050.005

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 head0.017
GPT teacher head0.254
Teacher spread0.236 · 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