Fibonacci Numbers and Decimation of Binary Sequences
نویسنده
چکیده
The problem of computing the number of sequences of various lengths that can be obtained by decimating a given binary sequence X of length n is considered. It is proven that this number is maximized iff X is an alternating sequence and that the maximum can be expressed in terms of the Fibonacci numbers. Some other upper bounds on this number are also determined, including another bound in terms of the Fibonacci numbers, depending on the run lengths in X.
منابع مشابه
Toeplitz transforms of Fibonacci sequences
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.
متن کاملA Class of Convergent Series with Golden Ratio Based on Fibonacci Sequence
In this article, a class of convergent series based on Fibonacci sequence is introduced for which there is a golden ratio (i.e. $frac{1+sqrt 5}{2}),$ with respect to convergence analysis. A class of sequences are at first built using two consecutive numbers of Fibonacci sequence and, therefore, new sequences have been used in order to introduce a new class of series. All properties of the se...
متن کاملA New Kind of Fibonacci-Like Sequence of Composite Numbers
An integer sequence (xn)n≥0 is said to be Fibonacci-like if it satisfies the binary recurrence relation xn = xn−1 + xn−2, n ≥ 2. We construct a new type of Fibonacci-like sequence of composite numbers. 1 The problem and previous results In this paper we consider Fibonacci-like sequences, that is, sequences (xn) ∞ n=0 satisfying the binary recurrence relation xn = xn−1 + xn−2, n ≥ 2. (1)
متن کاملPerformance of Fibonacci-Binary Sequences for SLM based OFDM Systems
Binary sequences such as chaotic-binary (CB) sequences derived from an iterative chaotic equation have been used in selected mapping (SLM) methods to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. Though CB sequences have been shown to produce good PAPR reduction performance, their implementation requires a significant number of compl...
متن کاملFibonacci sequence related to a combinatorial problem on binary matrices
We discuss an equivalence relation on the set of square binary matrices with the same number of 1’s in each row and each column. Each binary matrix is represented using ordered n-tuples of natural numbers. We give a few starting values of integer sequences related to the discussed problem. The obtained sequences are new and they are not described in the On-Line Encyclopedia of Integer Sequences...
متن کامل