On a conjecture about the strict Hall exponents of primitive matrices. (English) Zbl 0857.15007
Let \(B_n\) denote the set of all \(n \times n\) Boolean matrices. For \(A \in B_n\), the strict Hall exponent of \(A\), denoted by \(h(A)\), is the least positive integer \(k\) such that for every \(i \geq k\) \(A^i\) is a Hall matrix. A conjecture of Brualdi and Liu states that \(h(A) \leq [{n^2 \over 4}]\). The authors prove this conjecture completely.
Reviewer: A.Lal (Kanpur)
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