Baxter Tree-like Tableaux
Bibliographic record
Abstract
Tree-like tableaux are objects in bijection with alternative or permutation\ntableaux. They have been the subject of a fruitful combinatorial study for the\npast few years. In the present work, we define and study a new subclass of\ntree-like tableaux enumerated by Baxter numbers. We exhibit simple bijective\nlinks between these objects and three other combinatorial classes: (packed or\nmosaic) floorplans, twisted Baxter permutations and triples of non-intersecting\nlattice paths. From several (and unrelated) works, these last objects are\nalready known to be enumerated by Baxter numbers, and our main contribution is\nto provide a unifying approach to bijections between Baxter objects, where\nBaxter tree-like tableaux play the key role. We moreover get new enumerative\nresults about alternating twisted Baxter permutations. Finally, we define a new\nsubfamily of floorplans, which we call alternating floorplans, and we enumerate\nthese combinatorial objects.\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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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; both teacher heads agree on what is shown here.
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".