1. A. F. Horadam. "Basic Properties of a Certain Generalized Sequence of Numbers." The Fibonacci Quarterly 3 (1965):161-75. 2. A. F. Horadam. "Complex Fibonacci Numbers and Fibonacci Quaternions." Amer. Math. Monthly 70 (1963):289-91. 3. A. L. Iakin. "Generalized Quaternions with Quaternion Components." The Fibonacci Quarterly 15 (1977):35Q-52. 4. A. L. Iakin. "Generalized Quaternions of Higher...

The objective of this study was to develop a new optimal parallel algorithm for matrix multiplication which could run on a Fibonacci Hypercube structure. Most of the popular algorithms for parallel matrix multiplication can not run on Fibonacci Hypercube structure, therefore giving a method that can be run on all structures especially Fibonacci Hypercube structure is necessary for parallel matr...

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...

In this appendix we present an eecient implementation of the lter described in Section 3.1. One must place ciphertext diierences after (2r ?1)th round (one half-round before the last half-round) into DLevel + 1] and DLevel] before calling the lter. These diierences can be calculated (for RC5) from the known ciphertext diierences and the known rotation amount of the last round. A call to the lte...

The Fibonacci Cube is an interconnection network that possesses many desirable properties that are important in network design and application. The Fibonacci Cube can efficiently emulate many hypercube algorithms and uses fewer links than the comparable hypercube, while its size does not increase as fast as the hypercube. However, most Fibonacci Cubes (more than 2/3 of all) are not Hamiltonian....

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...