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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 n matrix with lcm(x_i , x_…
math.CO2014
A lattice-theoretic approach to the Bourque-Ligh conjecture
Ismo Korkee, Mika Mattila, Pentti Haukkanen
The Bourque-Ligh conjecture states that if 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]=[[…