A Note on Fibonacci Trees and the Zeckendorf Representation of Integers
نویسنده
چکیده
The Fibonacci numbers are defined, as usual9 by the recurrence F0 = 0, F1 = 1, Fk = Fk_x +Fk.z, k> 1. The Fibonacci tree of order k, denoted Tk, can be constructed inductively as follows: If k = 0 or k = 1, the tree is simply the root 0. If k > 15 the root is Fk ; the left subtree is Tjc_1; and the right subtree is Tk_2 with all node numbers increased by Fk . TG is shown in Figure 1. For an elegant role of the node numbers In the Fibonacci search algorithm3 the reader is referred to [5]. Fibonacci trees have been studied in detail by Horibe [2], [3]. The aim of this note is to present some additional considerations on Fibonacci tree codes and to explore the relationships existing between the codes and the Zeckendorf representation of integers.
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تاریخ انتشار 1986