A Recursive Algorithm to Generate Balanced Weekend Tournaments
Why this work is in the frame
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Bibliographic record
Abstract
In this paper, we construct a Balanced Weekend Tournament, motivated by the real-life problem of scheduling an n-team double round-robin season schedule for a Canadian university soccer league. In this 6-team league, games are only played on Saturdays and Sundays, with the condition that no team has two road games on any weekend. The implemented regular-season schedule for n = 6 was best-possible, but failed to meet an important "compactness" criterion, as the 10-game tournament required more than five weekends to complete. The motivation for this paper was to determine whether an optimal season schedule, satisfying all of the league's constraints on compact balanced play, could be constructed for sports leagues with n > 6 teams. We present a simple recursive algorithm to answer this question for all even n > 6. As a corollary, our construction gives us an explicit solution to a challenging and well-known graph theory question, namely the problem of decomposing the complete directed graph K*2m into 2m–1 directed Hamiltonian cycles of length 2m.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.002 |
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