DOIAbstract
AbstractIn a recent paper we proved that for an n×n matrix A with non-negative integer entries, there exist integers r,s with 0⩽r<s⩽2n such that Ar⩽As (cf. [Linear Algebra Appl. 290 (1999) 135]). Z. Bo [Austral. J. Combin. 21 (2000) 251] improved the bound 2n to 3n/2. We give two results in this paper. First, we improve the bound to n+g(n), where g is the Landau function. Thus we are close to the known lower bound of g(n) (cf. [Linear Algebra Appl. 290 (1999) 135]). Second, we show that if A is an irreducible matrix, then there is i=O(nlogn) such that Ai⩾I. We also give examples where i=Ω(nlogn/loglogn)
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