A Baxter class of a different kind, and other bijective results using\n tableau sequences ending with a row shape
Bibliographic record
Abstract
Tableau sequences of bounded height have been central to the analysis of\nk-noncrossing set partitions and matchings. We show here that familes of\nsequences that end with a row shape are particularly compelling and lead to\nsome interesting connections. First, we prove that hesitating tableaux of\nheight at most two ending with a row shape are counted by Baxter numbers. This\npermits us to define three new Baxter classes which, remarkably, do not\nobviously possess the antipodal symmetry of other known Baxter classes. We then\nconjecture that oscillating tableau of height bounded by k ending in a row are\nin bijection with Young tableaux of bounded height 2k. We prove this conjecture\nfor k at most eight by a generating function analysis. Many of our proofs are\nanalytic in nature, so there are intriguing combinatorial bijections to be\nfound.\n
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How this classification was reachedexpand
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) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".