تقرير
On the fibbinary numbers and the Wythoffarray
العنوان: | On the fibbinary numbers and the Wythoffarray |
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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. |