Symmetric pattern-avoiding permutations are restricted permutations which are invariant under actions of certain subgroups of D4, the symmetry group of a square. We examine pattern-avoiding permutations with 180◦ rotational-symmetry. In particular, we use combinatorial techniques to enumerate symmetric permutations which avoid one pattern of length three and one pattern of length four. Our resu...

We investigate the redundancy that arises from adding a worst case length constraint to uniquely decodable fixed-to-variable codes over achievable Huffman codes. This is in contrast to the traditional metric of the redundancy over the entropy. We show that the cost for adding constraints on the worst case coding length is small, and that the resulting bound is related to the Fibonacci numbers.

We investigate abelian repetitions in Sturmian words. We exploit a bijection between factors of Sturmian words and subintervals of the unitary segment that allows us to study the periods of abelian repetitions by using classical results of elementary Number Theory. If km denotes the maximal exponent of an abelian repetition of period m, we prove that lim sup km/m ≥ √ 5 for any Sturmian word, an...

A ((nite) Fibonacci string F n is deened as follows: F 0 = b, F 1 = a; for every integer n 2, F n = F n?1 F n?2. For n 1, the length of F n is denoted by f n = jF n j, while it is convenient to deene f 0 0. The innnite Fibonacci string F is the string which contains every F n , n 1, as a preex. Apart from their general theoretical importance, Fibonacci strings are often cited as worst case exam...

A ((nite) Fibonacci string F n is deened as follows: F 0 = b, F 1 = a; for every integer n 2, F n = F n?1 F n?2. For n 1, the length of F n is denoted by f n = jF n j. The innnite Fibonacci string F is the string which contains every F n , n 1, as a preex. Apart from their general theoretical importance, Fibonacci strings are often cited as worst case examples for algorithms which compute all t...

In this paper, we define the Fibonacci–Jacobsthal, Padovan–Fibonacci, Pell–Fibonacci, Pell–Jacobsthal, Padovan–Pell and Padovan–Jacobsthal sequences which are directly related with Fibonacci, Jacobsthal, Pell Padovan numbers give their structural properties by matrix methods. Then obtain new relationships between numbers.

We show that the Conway polynomials of Fibonacci links are Fibonacci polynomials modulo 2. We deduce that, when n 6≡ 0 (mod 4) and (n, j) 6= (3, 3), the Fibonacci knot F (n) j is not a Lissajous knot. keywords: Fibonacci polynomials, Fibonacci knots, continued fractions

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...