تقرير
On the fibbinary numbers and the Wythoffarray
| العنوان: | On the fibbinary numbers and the Wythoffarray |
|---|---|
| المؤلفون: | Macfarlane, A. J. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Mathematics - Number Theory, 11A67, 11B83 |
| الوصف: | This paper defines the set fib of fibbinary numbers and displays its structure in the form of a table of a specialised type, and in array form. It uses the Zeckendorf representation $n \in \mathbf{N}$ to define a bijection $\mathcal{Z}$ between $\mathbf{N}$ and fib. It is proved that the fibbinary array is the image under $\mathcal{Z}$ of the famous Wythoff array. The fibbinary table proves useful pictorial insight into the fractal defined by the Wythoff array. The Wythoff table, obtained as the image under the inverse of $\mathcal{Z}$ of the fibbinary table, leads to a simpler view of the fractal, and may be compared with the (1938) Steinhaus tree. Comment: 10 pages, 5 tables |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.18128 |
| رقم الأكسشن: | edsarx.2405.18128 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |