On exponent of indecomposability for primitive Boolean matrices

✍ Scribed by Bolian Liu

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 92 KB
• Volume: 298
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(99)00082-8

✦ Synopsis

Let rY n be integers, Àn r n, An n  n Boolean matrix A is called r-indecomposable if it contains no k  l zero submatrix with k l n À r 1. A is primitive if one of its powers, e k , has all positive entries for some integer k P 1. If A is primitive, then there is a smallest positive integer h r e k such that e k is r-indecomposable. There also is a smallest positive integer h à r e, such that e m is r-indecomposable for all m P h à r . h r and h à r are called exponent and strict exponent of r-indecomposability respectively. In this paper we obtain some new bounds of h à r e for primitive matrices and exact value of h à r e for symmetric primitive matrices.