Monotonic matrices and clique search in graphs

Abstract. Monotonic matrices are combinatorial objects defined in connection with certain questions in coding theory in [10]. It is an open problem to determine the maximum number of filled cells in an \(n\) by \(n\) monotonic matrix. In this note we determine this maximum value for \(7\leq n\leq 9\). The arguments are based partly on theoretical considerations and partly on computer aided exhaustive searches.