On meet and join matrices associated with incidence functions. (Q1410716)

Let \(P\) be a finite lattice, let \(S=\{x_1,\dots,x_n\}\), and let \(f\) be a complex-valued function on \(P\). The authors give a broad study of the matrices \((S)_f=[f(x_i\wedge x_j)]_{i,j}\) and \([S]_f=[f(x_i\vee x_j)]_{i,j}\), obtain upper and lower bounds for their determinants, and apply the obtained results to the study of the GCD-matrices and LCM-matrices, occurring in elementary number theory. This approach permits to obtain in a uniform way several known results about these matrices, and also to obtain new information about them.