Domino tableaux, Schützenberger involution, and the symmetric group action
Bibliographic record
Abstract
We define an action of the symmetric group S[n/2] on the set of domino tableaux, and prove that the number of domino tableaux of weight β′ does not depend on the permutation of the weight β′. A bijective proof of the well known result due to J. Stembridge that the number of self-evacuating tableaux of a given shape and weight β=(β1,…,β[(n+1)/2],β[n/2],…,β1), is equal to that of domino tableaux of the same shape and weight β′=(β1,…,β[(n+1)/2]) is given. Nous définissons une action du groupe symétrique S[n/2] sur l'ensemble des tableaux domino (‘domino tableaux’) et prouvons que le nombre de tableaux domino de poids β′ ne dépend pas de la permutation du poids β′. Une preuve bijective du résultat bien connu de J. Stembridge, voulant que le nombre de ‘self-evacuating tableaux’ d'une forme donnée et de poids β=(β1,…,β[(n+1)/2],β[n/2],…,β1) soit égal au nombre des tableaux domino de la même forme et de poids β=(β1,…,β[(n+1)/2]), est donnée.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".