AWavelet tree is a data structure adjoined to a file that has been compressed by a variable length encoding, which allows direct access to the underlying file, resulting in the fact that the compressed file is not needed any more. We adapt, in this paper, the Wavelet tree to Fibonacci Codes, so that in addition to supporting direct access to the Fibonacci encoded file, we also increase the comp...

We continue our study of the class of Fibonacci-automatic words. These are infinite words whose nth term is defined in terms of a finite-state function of the Fibonacci representation of n. In this paper, we show how enumeration questions (such as counting the number of squares of length n in the Fibonacci word) can be decided purely mechanically, using a decision procedure. We reprove some kno...

In lipid biochemistry, a fundamental question is how the potential number of fatty acids increases with their chain length. Here, we show that it grows according to the famous Fibonacci numbers when cis/trans isomerism is neglected. Since the ratio of two consecutive Fibonacci numbers tends to the Golden section, 1.618, organisms can increase fatty acid variability approximately by that factor ...

The paper investigates relationship between algebraic expressions and graphs. Through out the paper we consider two kinds of digraphs: series-parallel graphs and Fibonacci graphs (which give a generic example of non-series-parallel graphs). Motivated by the fact that the most compact expressions of series-parallel graphs are read-once formulae, and, thus, of O(n) length, we propose an algorithm...

In this paper, an efficient Fibonacci series based hierarchical protocolHFTM (Hierarchical Fibonacci Tree Multicast) is proposed for applicationlayer multicast. It adopts the idea of layer and cluster to construct multicast group members into a hierarchical architecture. During the cluster formation, it considers the underlying network properties to reduce packet delivering on costly links. In ...

Since their invention in the thirteenth century, Fibonacci sequences have intrigued mathematicians. As well as modeling the population patterns of overly energetic rabbits, however, they have sparked developments in more serious mathematics. For example, generalized Fibonacci sequences crop up in all manner of situations, from fiber optic networks [3] to computer algorithms [1] to probability t...

The problem of computing the number of sequences of various lengths that can be obtained by decimating a given binary sequence X of length n is considered. It is proven that this number is maximized iff X is an alternating sequence and that the maximum can be expressed in terms of the Fibonacci numbers. Some other upper bounds on this number are also determined, including another bound in terms...

A Lucas cube 3^ can be defined as the graph whose vertices are the binary strings of length n without either two consecutive l's or a 1 in the first and in the last position, and in which the vertices are adjacent when their Hamming distance is exactly 1. A Lucas cube 5E„ is very similar to the Fibonacci cube Tn which is the graph defined as 2J, except for the fact that the vertices are binary ...

The purpose of this paper is to study properties of mapped shuffled Fibonacci languages F(afi) and F^vy Let X — {a?6} be an alphabet and let X* be the free monoid generated by X. Let 1 be the empty word and let X+ — X* \ {1}. The length of a word u is denoted by lg(w). Every subset of X* is called a language. For two words u, v E X + ? we consider the following type of Fibonacci sequence of words:

Abstract—Study of fuzzy time series has increasingly attracted much attention due to its salient capabilities of tackling vague and incomplete data. A variety of forecasting models have devoted to improve forecasting accuracy. Recently, Fuzzy time-series based on Fibonacci sequence has been proposed as a new fuzzy time series model which incorporates the concept of the Fibonacci sequence, the f...