20 citations · 51 across the 19 of their papers we have counts for
23 papers
On generalized eigenvalues of MAX matrices to MIN matrices and of LCM matrices to GCD matrices
Jorma K. Merikoski, Pentti Haukkanen, Antonio Sasaki +1
We determine, for any n 1, the generalized eigenvalues of an n x n MAX matrix to the corresponding MIN matrix. We also show that a similar result holds for the generalized ei…
Some further applications of a lattice theoretic method in the study of singular LCM matrices
Mika Mattila, Pentti Haukkanen, Jori Mäntysalo
In 1876 H. J. S. Smith defined an LCM matrix as follows: let S = {x_1, x_2, ..., x_n} be a set of positive integers. The LCM matrix [S] is the n n matrix with lcm(x_i , x_…
Menon-type identities again: A note on a paper by Li, Kim and Qiao
Pentti Haukkanen, László Tóth
We give common generalizations of the Menon-type identities by Sivaramakrishnan (1969) and Li, Kim, Qiao (2019). Our general identities involve arithmetic functions of several vari…
Arithmetic Subderivatives and Leibniz-Additive Functions
Jorma K. Merikoski, Pentti Haukkanen, Timo Tossavainen
We first introduce the arithmetic subderivative of a positive integer with respect to a non-empty set of primes. This notion generalizes the concepts of the arithmetic derivative a…
Studying the inertias of LCM matrices and revisiting the Bourque-Ligh conjecture
Mika Mattila, Pentti Haukkanen, Jori Mäntysalo
Let be a finite set of distinct positive integers. Throughout this article we assume that the set is GCD closed. The LCM matrix of the set …
Positive definite functions on semilattices
Vesa Kaarnioja, Pentti Haukkanen, Pauliina Ilmonen +1
We introduce a notion of positive definiteness for functions defined on meet semilattices and prove several properties for these functions…