1. J. C. Butcher. "On a Conjecture Concerning a Set of Sequences Satisfying The Fibonacci Difference Equation/ The Fibonacci Quarterly 16 (1978):8183. 2. M. D. Hendy, "Stolarskys Distribution of Positive Integers." The Fibonacci Quarterly 16 (1978)2 70-80. 3. V. E. HoggattsJr. Fibonacci and Lucas Numbers* Boston: Houghton Mifflin9 1969. Pp. 34-35. 4. K. Stolarsky. "A Set of Generalized Fibonacc...

The generalized Fibonacci cube Qd(f) is the subgraph of the d-cube Qd induced on the set of all strings of length d that do not contain f as a substring. It is proved that if Qd(f) ∼= Qd(f ′) then |f | = |f ′|. The key tool to prove this result is a result of Guibas and Odlyzko about the autocorrelation polynomial associated to a binary string. An example of a family of such strings f , f ′, wh...

The generalized Fibonacci cube Qh(f) is the graph obtained from the h-cube Qh by removing all vertices that contain a given binary string f as a substring. In particular, the vertex set of the 3rd order generalized Fibonacci cube Qh(111) is the set of all binary strings b1b2 . . . bh containing no three consecutive 1’s. We present a new characterization of the 3rd order generalized Fibonacci cu...

This citizen science study evaluates the occurrence of Fibonacci structure in the spirals of sunflower (Helianthus annuus) seedheads. This phenomenon has competing biomathematical explanations, and our core premise is that observation of both Fibonacci and non-Fibonacci structure is informative for challenging such models. We collected data on 657 sunflowers. In our most reliable data subset, w...

This paper introduces a new interconnection network topology called Balanced Varietal Hypercube (BVH), suitable for massively parallel systems. The proposed topology being a hybrid structure retains almost all the attractive properties of Balanced Hypercube and Varietal Hypercube. The topology, various parameters, routing and broadcasting of Balanced Varietal Hypercube are presented. The perfor...

Five new classes of Fibonacci-Hessenberg matrices are introduced. Further, we introduce the notion of two-dimensional Fibonacci arrays and show that three classes of previously known Fibonacci-Hessenberg matrices and their generalizations satisfy this property. Simple systems of linear equations are given whose solutions are Fibonacci fractions.

The Fibonacci dimension fdim(G) of a graph G was introduced in [1] as the smallest integer d such that G admits an isometric embedding into Γd, the d-dimensional Fibonacci cube. The Fibonacci dimension of the resonance graphs of catacondensed benzenoid systems is studied. This study is inspired by the fact, that the Fibonacci cubes are precisely the resonance graphs of a subclass of the catacon...

As in [1, 2], for rapid numerical calculations of identities pertaining to Lucas or both Fibonacci and Lucas numbers we present each identity as a binomial sum. 1. Preliminaries The two most well-known linear homogeneous recurrence relations of order two with constant coefficients are those that define Fibonacci and Lucas numbers (or Fibonacci and Lucas sequences). They are defined recursively ...