Determinants of matrices of the conference type
An \(n\) by \(n\) conference type matrix has \(0\)'s on the main diagonal and \(\pm 1\)'s elsewhere. The authors investigate the largest possible determinant of such a matrix for \(n\) odd, \(n \leq 11.\) For \(n\) even, there is already an extensive literature but even there a few conjectures are still open. To get the matrices having largest determinant among conference matrices for \(n\) odd, \(n \leq 11,\) the authors use some intelligent techniques which help them in reducing their search drastically. The same techniques don't seem to work for higher values of \(n\). And even with their intelligent technique they had to use a huge CPU time. So, the problem seems to be very very difficult for large odd \(n\). At the end, I would like to add that their notation `P-matrix' (in honor of Paley) for certain matrices doesn't seem appropriate as this notation has already been accepted long back for certain class of matrices in the literature on Linear Complementarity Problem in Operations Research.
scientific article; zbMATH DE number 1044260