Mika Mattila

activity

20112022

most citedOn the eigenvalues of combined meet and join matrices

12 citations · 19 across the 8 of their papers we have counts for

collaborators

11 papers

math.CO2022

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 $\times$ n matrix with lcm(x_i , x_…

math.NT2018

Studying the inertias of LCM matrices and revisiting the Bourque-Ligh conjecture

Mika Mattila, Pentti Haukkanen, Jori Mäntysalo

Let $S = {x_{1}, x_{2}, \dots, x_{n}}$ be a finite set of distinct positive integers. Throughout this article we assume that the set $S$ is GCD closed. The LCM matrix $[S]$ of the set $S$ …

math.NT2018

Positive definite functions on semilattices

Vesa Kaarnioja, Pentti Haukkanen, Pauliina Ilmonen +1

We introduce a notion of positive definiteness for functions $f : P \to R$ defined on meet semilattices $(P, ⪯, \land)$ and prove several properties for these functions…

math.NT2017★ 2 cited

The spectral norm of a Horadam circulant matrix

Jorma K. Merikoski, Pentti Haukkanen, Mika Mattila +1

Let $a$ , $b$ , $p$ , $q$ be integers and~ $(h_{n})$ defined by $h_{0} = a$ , $h_{1} = b$ , $h_{n} = p h_{n - 1} + q h_{n - 2}$ , $n = 2, 3, \dots$ . Complementing to certain previously known results, we study the…

math.CO2014

A lattice-theoretic approach to the Bourque-Ligh conjecture

Ismo Korkee, Mika Mattila, Pentti Haukkanen

The Bourque-Ligh conjecture states that if $S = {x_{1}, x_{2}, \dots, x_{n}}$ is a gcd-closed set of positive integers with distinct elements, then the LCM matrix $[S]=[\hbox{lcm}(x_i,x_j)…

math.CO2014

Studying the singularity of LCM-type matrices via semilattice structures and their Möbius functions

Mika Mattila, Pentti Haukkanen, Jori Mäntysalo

The invertibility of LCM matrices and their Hadamard powers have been studied a lot over the years by many authors. Bourque and Ligh conjectured in 1992 that the LCM matrix $[S]=[[…

math.NT2014★ 12 cited

On the eigenvalues of combined meet and join matrices

Mika Mattila

In this article we give bounds for the eigenvalues of a matrix, which can be seen as a common generalization of meet and join matrices and therefore also as a generalization of bot…

math.NT2013★ 5 cited

On the eigenvalues of certain number-theoretic matrices

Mika Mattila, Pentti Haukkanen

In this paper we study the structure and give bounds for the eigenvalues of the $n \times n$ matrix, which $ij$ entry is $(i, j)^{α} [i, j]^{β}$ , where $α,β\in\Rset$, $(i, j)$ is the greate…

math.NT2012

On the positive definiteness and eigenvalues of meet and join matrices

Mika Mattila, Pentti Haukkanen

In this paper we study the positive definiteness of meet and join matrices using a novel approach. When the set $S_{n}$ is meet closed, we give a sufficient and necessary condition f…

math.NT2011

Some properties of row-adjusted meet and join matrices

Mika Mattila, Pentti Haukkanen

Let $(P, ⪯)$ be a lattice, $S$ a finite subset of $P$ and $f_{1}, f_{2}, ..., f_{n}$ complex-valued functions on $P$ . We define row-adjusted meet and join matrices on $S$ by $(S)_{f_1,…

math.NT2011

Determinant and inverse of join matrices on two sets

Mika Mattila, Pentti Haukkanen

Let $(P, ⪯)$ be a lattice and $f$ a complex-valued function on $P$ . We define meet and join matrices on two arbitrary subsets $X$ and $Y$ of $P$ by $(X,Y)_f=(f(x_i\wedge y_j))…