Algebraic properties of finite simple groups via the (r,k)-bonacci sequence and more
Bibliographic record
Abstract
The main goal of this paper is to determine algebraic properties of finite groups via the [Formula: see text]-bonacci sequences. First, we give the relationships between the [Formula: see text]-bonacci numbers, the Fibonacci-[Formula: see text] numbers, the Narayana numbers, and the [Formula: see text]-generalized order-[Formula: see text] Perrin numbers. Then, we study the [Formula: see text]-bonacci numbers modulo [Formula: see text] and give some results concerning the periods of the [Formula: see text]-bonacci sequences for any [Formula: see text] and [Formula: see text]. In addition, we extend the [Formula: see text]-bonacci sequences to [Formula: see text]-generator groups and investigate these sequences in finite groups. Finally, we obtain the periods of the [Formula: see text]-bonacci sequences in well-known classes of finite groups as an application of the results obtained.
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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 | 0.000 |
| 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".