We examine the Fibonacci lengths of all generating pairs for certain centro-polyhedral groups. The problem requires a variety of approaches both exhaustive and random search. 1991 Mathematics Subject Classification: 20F05.

The problem we investigate deals with the optimal assignment of resources to the activities of a stochastic project network. We seek to minimize the expected cost of the project include sum of resource utilization costs and lateness costs. We assume that the work content required by the activities follows an exponential distribution. The decision variables of the model are the allocated resourc...

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...

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we introduce a matricial toeplitz transform and prove that the toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. we investigate the injectivity of this transform and show how this distinguishes the fibonacci sequence among other recurrence sequences. we then obtain new fibonacci identities as an application of our transform.

We provide explicit formulas for the maximum number qk(n) of disjoint subgraphs isomorphic to the k-dimensional hypercube in the n-dimensional Fibonacci cube Γn for small k, and prove that the limit of the ratio of such cubes to the number of vertices in Γn is 1 2k for arbitrary k. This settles a conjecture of Gravier, Mollard, Špacapan and Zemljič about the limiting behavior of qk(n).

By using antitrace map method, we investigate the light transmission for a generalized Fibonacci multilayers. Analytical results are obtained for transmission coefficients in some special cases. We find that the transmission coefficients possess two-cycle property or six-cycle property. The cycle properties of the trace and antitrace are also obtained. PACS numbers: 61.44.Br, 05.45.-a, 42.25.Dd...