Maximal Determinants In Combinatorial Investigations

Introduction. Let Q be a matrix of order v, all of whose entries are 0's and l's. Let the total number of l's in Q be t , and let the absolute value of the determinant of Q be denoted by |det Q |. In this paper we study the problem of determining the maximum of |det Q | for fixed t and v. It turns out that this problem is closely related to the v , k , λ problem, which has been extensively studied of late.