SORTING SIGNED PERMUTATIONS BY FIXED-LENGTH REVERSALS
Why this work is in the frame
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Bibliographic record
Abstract
A signed n-permutation is a permutation on {1,2,…,n} in which each element is labelled by a positive or negative sign. Here we consider the problem of sorting signed permutations by fixed-length reversals. Indeed, limiting the transformations to reversals of length exactly k can be very restrictive, for example, (+1,+3,+2,+4,…,+n) can never be sorted to (+1,+2,+3,+4,…,+n) by 2-reversals. That is, for given two signed permutations it is not obvious whether they can be sorted to each other by k-reversals. Thus in 1996, Chen and Skiena gave the following open problem: what is the connectedness of signed permutations under fixed-length reversals? In this paper, we resolve this open problem when "fixed-length" is even, and give a characterization of the connectedness of signed n-permutations under 2l-reversal, for both linear and circular permutations.
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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 | 0.001 | 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 it