Fibonacci sequence related to a combinatorial problem on binary matrices
نویسنده
چکیده
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 (OEIS). We show a relationship between some particular values of the parameters and the Fibonacci sequence. Keyword: binary matrix; equivalence relation; factor-set; Fibonacci number 2010 Mathematics Subject Classification: 05B20; 11B39
منابع مشابه
An application of Fibonacci numbers into infinite Toeplitz matrices
The main purpose of this paper is to define a new regular matrix by using Fibonacci numbers and to investigate its matrix domain in the classical sequence spaces $ell _{p},ell _{infty },c$ and $c_{0}$, where $1leq p
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 کاملFactor-set of binary matrices and Fibonacci numbers
The article discusses the set of square n n binary matrices with the same number of 1’s in each row and each column. An equivalence relation on this set is introduced. Each binary matrix is represented using ordered n-tuples of natural numbers. We are looking for a formula which calculates the number of elements of each factor-set by the introduced equivalence relation. We show a relationship b...
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 کاملFibonacci Numbers and Decimation of Binary Sequences
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...
متن کامل