Triangular blocks of zeros in (0, 1) matrices with small permanents Original Research Article

Let A be a square matrix and t a positive integer. We say A is t-triangular if there exist permutation matrices P and Q such that PAQ = B = [bij] has bij = 0 whenever j greater-or-equal, slanted i + t. We ask for which positive integers the following statement is true: If A is any square matrix with nonnegative integral entries such that 0 < per A < (t + 1)!, then A is t-triangular. If t = 1, the statement reduces to a theorem of Brualdi. We prove the statement is true for t = 2 and t = 3, but false for t = 6.