Maximum permanents of matrices of zeros and ones (Q1104376)

Let A be a 0,1-matrix of order n with t zeros. The main results of this paper are contained in three theorems. The first establishes an upper bound on per(A) as a function of n and t. The second obtains the least upper bound on per(A) and characterizes the matrices that realize it, for \(n\geq 3\) and n 2-2n\(\leq t\leq n\) 2-n. (Note: per A\(=0\) if \(t>n\) 2-n.) The third characterizes the matrices that achieve the least upper bound on per(A), for \(n\geq 3\) and \(0\leq t\leq 2n\). The proofs rely heavily on partitioned matrices.