Why this work is in the frame
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Bibliographic record
Abstract
We show that formulae of Gessel for the generating functions for Young standard tableaux of height bounded by k (see [2]) satisfy linear differential equations, with polynomial coefficients, equivalent to P - recurrences conjectured by Favreau, Krob and the first author (see [1]) for the number of bounded height tableaux and pairs of bounded height tableaux. 1. Results Let us first fix some notation. A partition of a positive integer n is a sequence of integers 1 2 : : : k ? 0 such that P i i = n. We denote this by writing ` n, and say that k is the height h() of . The height of the empty partition (of 0) is 0. The (Ferrer's) diagram of a partition is the set of points (i; j) 2 Z 2 such that 1 j i . It is also denoted by . Clearly a partition is characterized by its diagram. The conjugate 0 of a partition is the partition with diagram f(j; i) j (i; j) 2 g. A standard Young tableau T is an injective labeling of a Ferrer's diagram by the elements of f1; 2; : : : ...
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Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it