Maximum permanents of matrices of zeros and ones

Abstract Let U (n, τ) be the set of all matrices of 0′s and 1′s of order n with exactly τ 0′s. We obtain an upper bound for the permanent of a matrix in U (n, τ). For 0⩽τ⩽2n and for n2 − 2n⩽τ⩽n2 − n we determine all matrices in U (n, τ) with maximum permanent.