Jori Mäntysalo

Jori Mäntysalo
Tampere University | UTA · School of Information Sciences

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5
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Introduction
Skills and Expertise

Publications

Publications (5)
Preprint
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_j) as its ij entry. During the last 30 years singularity of LCM matrices has interested many authors. In 1992 Bourque and Ligh ended up conjecturing that if the GCD close...
Article
Let S={x1,x2,…,xn} 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 is defined to be the n×n matrix with lcm(xi,xj) as its ij element. The famous Bourque-Ligh conjecture used to state that the LCM matrix of a GCD closed set S is always invertible, but curr...
Preprint
Full-text available
Let $S=\{x_1,x_2,\ldots,x_n\}$ be a finite subset of distinct positive integers. Throughout this article we also assume that our set $S$ is GCD closed. The LCM matrix $[S]$ of the set $S$ is defined to be the $n\times n$ matrix with $\mathrm{lcm}(x_i,x_j)$ as its $ij$ element. The famous Bourque-Ligh conjecture used to state that the LCM matrix of...
Article
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 $[S]=[[x_i, x_j]]$ on any GCD closed set $S=\{x_1, x_2, \ldots, x_n\}$ is invertible, but in 1997 this was proven false. However, currently there are many open conjectures conce...

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