On Families Of Bipartite Graphs Associated With Sums Of Generalized Order-k Fibonacci And Lucas Numbers.
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
In this paper, we consider the relationships between the sums of the generalized order-k Fibonacci and Lucas numbers and 1-factors of bipartite graphs. 1. Introduction We consider the generalized order k Fibonacci and Lucas numbers. In [1], Er de ned k sequences of the generalized order k Fibonacci numbers as shown: g n = k X j=1 g n j ; for n > 0 and 1 i k; (1.1) with boundary conditions for 1 k n 0; g n = 1 if i = 1 n; 0 otherwise, where g n is the nth term of the ith sequence. For example, if k = 2, then g n is usual Fibonacci sequence, fFng ; and, if k = 4, then the 4th sequence of the generalized order 4 Fibonacci numbers is 1; 1; 2; 4; 8; 15; 29; 56; 108; 208; 401; 773; 1490; : : : : In [9], the authors de ned k sequences of the generalized order k Lucas numbers as shown: l n = k X j=1 l n j , for n > 0 and 1 i k, (1.2) 2000 Mathematics Subject Classi cation. 11B39, 15A15, 15A36, 05C50.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 it