On a conjecture about the strict Hall exponents of primitive matrices

Let Bn denote the set of n×n Boolean matrices. For A=(aij), B=(bij)∈Bn, if aij≤bij, i. j= 1, 2, '', n. we say A≤B. An n×n Boolean matrix A is called primitive if there exists some positive integer k such that Ak=Jn, the all l’s matrix in Bn. Such a least positive integer k is called the exponent of A, denoted by γ（A）. Let Pn denote the set of all n×n primitive matrices in Bn. A matrix A∈Bn is called a Hall matrix if there exists some permutation matrix Q such that Q≤A.