Results 11 to 20 of about 218 (36)

Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions

Open Mathematics, 2016
Let f be an arithmetic function and S= {x1, …, xn} be a set of n distinct positive integers. By (f(xi, xj)) (resp. (f[xi, xj])) we denote the n × n matrix having f evaluated at the greatest common divisor (xi, xj) (resp. the least common multiple [xi, xj]
Hong Siao, Hu Shuangnian, Hong Shaofang
doaj   +1 more source

Inertia, positive definiteness and $\ell_p$ norm of GCD and LCM matrices and their unitary analogs [PDF]

, 2017
Let $S=\{x_1,x_2,\dots,x_n\}$ be a set of distinct positive integers, and let $f$ be an arithmetical function. The GCD matrix $(S)_f$ on $S$ associated with $f$ is defined as the $n\times n$ matrix having $f$ evaluated at the greatest common divisor of ...
Haukkanen, Pentti, Tóth, László
core   +2 more sources

Fibonacci and Telephone Numbers in Extremal Trees

Discussiones Mathematicae Graph Theory, 2018
In this paper we shall show applications of the Fibonacci numbers in edge-coloured trees. In particular we determine the successive extremal graphs in the class of trees with respect to the number of (A, 2B)-edge colourings.
Bednarz Urszula, Włoch Iwona
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On Generalized Jacobsthal and Jacobsthal-Lucas polynomials

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016
In this paper we introduce a generalized Jacobsthal and Jacobsthal-Lucas polynomials, Jh,n and jh,n, respectively, that consist on an extension of Jacobsthal's polynomials Jn(𝑥) and Jacobsthal-Lucas polynomials jn(𝑥).
Catarino Paula, Morgado Maria Luisa
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Jacobsons Lemma fails for nil-clean 2 × 2 integral matrices

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020
We show that for two 2 × 2 integral matrices A, B, if the product AB is nil-clean then BA may not be nil-clean. Despite the fact that for many special cases, BA is also nil-clean, we finally found three counterexamples.
Călugăreanu Grigore, Pop Horia F.
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On generalizations of two curious divisibility properties

, 2013
In this paper, we extend two curious divisibility properties for the general second order linear recurrence fUn.p;q/g. We also give new recursive identities for the general second linear recurrences fUn.p;q/g and fVn.p;q/g.
Aynur Yalçiner
semanticscholar   +1 more source

Rank relations between a {0, 1}-matrix and its complement

Open Mathematics, 2018
Let A be a {0, 1}-matrix and r(A) denotes its rank. The complement matrix of A is defined and denoted by Ac = J − A, where J is the matrix with each entry being 1.
Ma Chao, Zhong Jin
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A MATRIX APPROACH FOR GENERALIZING TWO CURIOUS DIVISIBILITY PROPERTIES

, 2012
We shall consider two curious divisibility properties due to (1, 5). Our main purpose is to generalize these properties for a general second order linear recursion. We use generating matrix approach for our purposes. By using our results, we derive a new
E. Kılıç
semanticscholar   +1 more source

Generalized Pell Equations for 2 × 2 Matrices

Discussiones Mathematicae - General Algebra and Applications, 2017
In this paper we consider the solutions of the generalized matrix Pell equations X2 − dY2 = cI, where X and Y are 2 × 2 matrices over ℤ, d is a non-zero (positive or negative) square-free integer, c is an arbitrary integer and I is the 2 × 2 identity ...
Cohen Boaz
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NEW STRUCTURES IN PSEUDO MAGIC SQUARES

, 2019
A pseudo magic square (PMS) of order n is an n×n square matrix whose entries are integers such that the sum of the numbers of any row and any column is the same number, the magic constant. It is a generalization of the concept of magic squares.
G. L. Guardia
semanticscholar   +1 more source