We present a bound on the exponent exp(A) of an n X n primitive matrix A in terms of its boolean rank b = b(A); namely exp(A) less than or equal to (b - 1)(2) + 2. Further, we show that for each 2 less than or equal to b less than or equal to n - 1, there is an n X n primitive matrix A with b(A)= b such that exp(A) = (b - 1)(2) + 2, and we explicitly describe all such matrices. The new bound is compared with a well-known bound of Dulmage and Mendelsohn, and with a conjectured bound of Hartwig and Neumann. Several open problems are posed. [References: 8]
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机译：我们用布尔等级b = b（A）表示n X n基本矩阵A的指数exp（A）的界。即exp（A）小于或等于（b-1）（2）+2。此外，我们证明对于小于或等于b的每2个小于或等于n-1的对象，存在一个n X n基本矩阵A的b（A）= b使得exp（A）=（b-1）（2）+ 2，我们明确地描述了所有这样的矩阵。将新界限与著名的Dulmage和Mendelsohn界限以及推测的Hartwig和Neumann界限进行比较。提出了几个未解决的问题。 [参考：8]
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