A weak repetition in a string consists of two or more adjacent substrings which are permutations of each other. We describe a straightforward (n 2) algorithm which computes all the weak repetitions in a given string of length n deened on an arbitrary alphabet A. Using results on Fibonacci and other simple strings, we prove that this algorithm is asymptotically optimal over all known encodings o...

We consider an algorithmic problem of computing the first, i.e., the most meaningful digits of 2 (at base 3) and of the nth Fibonacci number. While the decidability is trivial, efficient algorithms for those problems are not immediate. We show, based on Baker’s inapproximability results of transcendental numbers that both of the above problems can be solved in polynomial time with respect to th...

This paper develops a closed-form formula, f ( k ), to count the number of transition-tour sequences of length k for bistable machines. It is shown that the function f ( k ) is related to Fibonacci numbers. Some applications of the results in this paper are in the areas of: testable sequential machine designs, random testing of register data paths, and qualification tests for random pattern gen...

In 2001, Shimozono and White gave a description of the domino Schensted algorithm of Barbasch, Vogan, Garfinkle and van Leeuwen with the “color-to-spin” property, that is, the property that the total color of the permutation equals the sum of the spins of the domino tableaux. In this paper, we describe the poset of domino Fibonacci shapes, an isomorphic equivalent to Stanley’s Fibonacci lattice...

The Fibonacci cube Γn is a subgraph of n-dimensional hypercube induced by the vertices without two consecutive ones. Klavžar and Žigert [Fibonacci cubes are the resonance graphs of fibonaccenes, Fibonacci Quart. 43 (2005) 269–276] proved that Fibonacci cubes are precisely the Z -transformation graphs (or resonance graphs) of zigzag hexagonal chains. In this paper, we characterize plane bipartit...

Let Γn and Λn be the n-dimensional Fibonacci cube and Lucas cube, respectively. The domination number γ of Fibonacci cubes and Lucas cubes is studied. In particular it is proved that γ(Λn) is bounded below by ⌈ Ln−2n n−3 ⌉ , where Ln is the n-th Lucas number. The 2-packing number ρ of these cubes is also studied. It is proved that ρ(Γn) is bounded below by 2 blg nc 2 −1 and the exact values of ...

In this work, we propose a CODEC design for the forbidden transition free crosstalk avoidance CODEC. Our mapping and coding scheme is based on the binary number system. In this paper we investigate and propose a bus forbidden transition free CODECs for reducing bus delay and our experimental results shows that the proposed CODEC complexity is orders of magnitude better compared to the existing ...

The aim of this note is to survey the factorizations of the Fibonacci infinite word that make use of the Fibonacci words and other related words, and to show that all these factorizations can be easily derived in sequence starting from elementary properties of the Fibonacci numbers. 1 Preliminaries The well-known sequence of Fibonacci numbers (sequence A000045 in the On-Line Encyclopedia of Int...

Various generalizations of the Fibonacci numbers have been proposed, studied and applied over the years (see [5] for a brief list). Probably the best known are the k-generalized Fibonacci numbers F (k) n (also known as the k-fold Fibonacci, k-th order Fibonacci, k-Fibonacci or polynacci numbers), satisfying F (k) n = F (k) n−1 + F (k) n−2 + . . .+ F (k) n−k , n ≥ k , F (k) n = 0 , 0 ≤ n ≤ k − 2...

The Fibonacci operator approach inspired by Andrews (2004) is explored to investigate q-analogs of the generalized Fibonacci and Lucas polynomials introduced by Chu and Vicenti (2003). Their generating functions are compactly expressed in terms of Fibonacci operator fractions. A determinant evaluation on q-binomial coefficients is also established which extends a recent result of Sun (2005).