Two diierent factorizations of the Fibonacci innnite word were given independently in 10] and 6]. In a certain sense, these factorizations reveal a self-similarity property of the Fibonacci word. We rst describe the intimate links between these two factorizations. We then propose a generalization to characteristic sturmian words. R esum e. Deux factorisations du mot de Fibonacci ont et e donn e...

In this paper, we introduce the h-analogue of Fibonacci numbers for non-commutative h-plane. For hh = 1 and h = 0, these are just the usual Fibonacci numbers as it should be. We also derive a collection of identities for these numbers. Furthermore, h-Binet’s formula for the h-Fibonacci numbers is found and the generating function that generates these numbers is obtained. 2000 Mathematical Subje...

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 ele...

We show that if w is a factor of the infinite Fibonacci word, then the least period of w is a Fibonacci number.

In this study, new properties of Fibonacci numbers is given. Also, generalization of some properties of Fibonacci numbers is investigated with binomial coefficiations. Mathematics Subject Classification: 11B39, 11B65

We present some binomial identities for sums of the bivariate Fi-bonacci polynomials and for weighted sums of the usual Fibonacci polynomials with indices in arithmetic progression.

Knuth [12, Page 417] states that “the (program of the) Fibonaccian search technique looks very mysterious at first glance” and that “it seems to work by magic”. In this work, we show that there is even more magic in Fibonaccian (or else Fibonacci) search. We present a generalized Fibonacci procedure that follows perfectly the implicit optimal decision tree for search problems where the cost of ...

What are generally referred to as the Fibonacci numbers and the method for their formation were given by Virahanka (between A.D. 600 and X00). Gopala (prior to A.D. 1135) and Hemacandra (c. A.D. 1150). all prior to L. Fibonacci (c. A.D. 1202). Narayana Pandita (A.D. 13Sh) established a relation between his srftcisi~ci-pcrirLfi. which contains Fibonacci numbers as a particular case. and “the mul...

After defining a class of generalized Fibonacci numbers and Lucas numbers, we characterize the Fibonacci pseudoprimes of the mth kind. In virtue of the apparent paucity of the composite numbers which are Fibonacci pseudoprimes of the mth kind for distinct values o f the integral parameter m , a method, which we believe to be new, for finding large probable primes is proposed. An efficient compu...

The purpose of this paper is to investigate the calculation of Fibonacci numbers using the Chinese Remainder Theorem (CRT). This paper begins by laying down some general conclusions that can be made about the Fibonacci sequence. It will then go into specific cases of the CRT and how to calculate Fibonacci numbers with reduced forms of the CRT equations. For each of the cases, algorithms and ana...