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

Massively parallel distributed-memory architectures are receiving increasing attention to meet the increasing demand on processing power. Many topologies have been proposed for interconnecting the processors of distributed computing systems. The hypercube topology has drawn considerable attention due to many of its attractive properties. The appealing properties of the hypercube topology such a...

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...

Families of Fibonacci codes and Fibonacci representations are defined. Their main attributes are: (i) robustness, manifesting itself by the local containment of errors; (ii) simple encoding and and decoding. The main applica· tiOD explored is the transmission of binary strings whose length is in aD. unknown range, using robust Fibonacci representations instead of the conventional errorsensitive...