On (−1, 1)-Matrices of Skew Type with the Maximal Determinant and Tournaments

Abstract

Skew Hadamard matrices of order n give the solution to the question of finding the largest possible n by n determinant with entries ± 1 of skew type when n≡0(mod4) . Characterizations of skew Hadamard matrices in terms of tournaments are well-known. For n≡2(mod4) , we give a characterization of (−1, 1)-matrices of skew type of order n where their determinants reach Ehlich–Wojtas’ bound in terms of tournaments.