On the maximum of the permanent of (I − A)

Let ωns and ω˜ns denote the convex sets of n×n doubly substochastic matrices and row substochastic matrices with the sum of all entries equal to s, respectively. In this paper, we give the upper bound of the permanent of I−A for A∈ω˜ns. We also give the upper bound of the permanent of I−A for A∈ωns, where either n is even, or n is odd and s≤n−1. For the case when n is odd and n−1