منابع مشابه
Divisibilty Properties of Gcd Ve Lcm Matrices
Let a, b and n be positive integers and let S = {x1, x2, . . . , xn} be a set of distinct positive integers. The n × n matrix (Sf ) = (f ((xi, xj))), having f evaluated at the greatest common divisor (xi, xj) of xi and xj as its ij−entry, is called the GCD matrix associated with f on the set S. Similarly, the n × n matrix [Sf ] = (f ([xi, xj ])) is called the LCM matrix associated with f on S. ...
متن کاملNotes on the divisibility of GCD and LCM Matrices
Let S = {x1,x2, . . . ,xn} be a set of positive integers, and let f be an arithmetical function. The matrices (S) f = [ f (gcd(xi,xj))] and [S] f = [ f (lcm[xi,xj])] are referred to as the greatest common divisor (GCD) and the least common multiple (LCM) matrices on S with respect to f , respectively. In this paper, we assume that the elements of the matrices (S) f and [S] f are integers and st...
متن کاملGcd Matrices, Posets, and Nonintersecting Paths
We show that with any finite partially ordered set, P , one can associate a matrix whose determinant factors nicely. As corollaries, we obtain a number of results in the literature about GCD matrices and their relatives. Our main theorem is proved combinatorially using nonintersecting paths in a directed graph.
متن کاملON THE `p NORM OF GCD AND RELATED MATRICES
We estimate the `p norm of the n×n matrix, whose ij entry is (i, j)/[i, j], where r, s ∈ R, (i, j) is the greatest common divisor of i and j and [i, j] is the least common multiple of i and j.
متن کاملDeterminants and permanents of Hessenberg matrices and generalized Lucas polynomials
In this paper, we give some determinantal and permanental representations of generalized Lucas polynomials, which are a general form of generalized bivariate Lucas p-polynomials, ordinary Lucas and Perrin sequences etc., by using various Hessenberg matrices. In addition, we show that determinant and permanent of these Hessenberg matrices can be obtained by using combinations. Then we show, the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1990
ISSN: 0024-3795
DOI: 10.1016/0024-3795(90)90012-2