A Fibonacci string of order n is a binary string of length n with no two consecutive ones. The Fibonacci cube n is the subgraph of the hypercube Qn induced by the set of Fibonacci strings of order n. For positive integers i; n, with n¿ i, the ith extended Fibonacci cube is the vertex induced subgraph of Qn for which V ( i n) = V i n is de2ned recursively by V i n+2 = 0V i n+1 + 10V i n; with in...

In this paper we introduce a family of infinite words that generalize the Fibonacci word and we study their combinatorial properties. We associate with this family of words a family of curves that are like the Fibonacci word fractal and reveal some fractal features. Finally, we describe an infinite family of polyominoes stems from the generalized Fibonacci words and we study some of their geome...

PURPOSE The motion path of the digits follows the path of an equiangular spiral in which a constant angle is formed by all radial vectors along the curve. This implies that the lengths of the metacarpals, proximal, middle, and distal phalanges approximate a Fibonacci sequence in which the ratio of any 2 consecutive numbers approaches the number 1.61803 (phi). This study tested the hypothesis th...

Abstract It is known that binary words containing no k consecutive 1s are enumerated by -step Fibonacci numbers. In this note we discuss the expected value of a random bit in word length n having property.

The Fibonacci (p, r)-cube is an interconnection topology, which includes a wide range of connection topologies as its special cases, such as the Fibonacci cube, the postal network, etc. Klavžar and Žigert [S. Klavžar, P. Žigert, Fibonacci cubes are the resonance graphs of fibonaccenes, Fibonacci Quart. 43 (2005) 269–276] proved that Fibonacci cubes are just the Z-transformation graphs (also cal...

We study q-analogues of k-Fibonacci numbers that arise from weighted tilings of an n × 1 board with tiles of length at most k. The weights on our tilings arise naturally out of distributions of permutations statistics and set partitions statistics. We use these q-analogues to produce q-analogues of identities involving k-Fibonacci numbers. This is a natural extension of results of the first aut...

0

Here, we find all instances in which a product of Fibonacci numbers with indices in an interval of length k and at most four of them omitted is a perfect power.

The principal conclusion is that Fibonacci phyllotaxis follows as a mathematical necessity from the combination of an expanding apex and a suitable spacing mechanism for positioning new leaves. I have considered an inhibitory spacing mechanism at some length, as it is a plausible candidate. However, the same treatment would apply equally well to depletion of, or competition for, a compound by d...

A helpful starting point is the paper entitled "Fibonacci Series Modulo m by D. D. Wall [3]. With Wall, we let /„ denote the n member of the sequence of integers fQ = a, f1 = b9 ..., where fn + 1 = fn + f n _ r The symbol h(m) will denote the length of the period of the sequence resulting from reducing each /„ modulo w. The basic Fibonacci sequence will be given by uQ = 0, ux = 1, ... and the L...