✦ LIBER ✦

On the exponent of a primitive matrix containing a primitive submatrix

✍ Scribed by LeRoy B. Beasley; Steve Kirkland

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 713 KB
Volume: 261
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(96)00401-6

No coin nor oath required. For personal study only.

✦ Synopsis

For a primitive matrix A of order n + k having a primitive submatrix of order 71, we prove that the exponent of A is at most (n -1)" + 2k + 1. We characterize those matrices attaining the bound in terms of their directed graphs, and explicitly describe those graphs for the case that k < 2n.

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## Abstract In this paper the conjecture on the __k__th upper multiexponent of primitive matrices proposed by R.A. Brualdi and Liu are completely proved.