On the exponent of r-regular primitive matrices

• Tipo: Artigo em Revista Científica Internacional
• Data: 2008

Autores

Maria Isabel Bueno (Autor) Outra; Susana Borges Furtado (Autor) FEP

Revista

Título: Electronic Journal of Linear Algebra

Vol. 17

Páginas: 28-47

ISSN: 1537-9582

Editora: INT LINEAR ALGEBRA SOC

Indexação

ISI Web of Knowledge - 4 Citações

ISI Web of Science

Scopus - 4 Citações

Classificação Científica

FOS: Ciências exactas e naturais

Outras Informações

ID Authenticus: P-004-342

Abstract (EN): Let P-nr be the set of n-by-n r-regular primitive (0,1)-matrices. In this paper, an explicit formula is found in terms of n and r for the minimum exponent achieved by matrices in P-nr. Moreover, matrices achieving that exponent are given in this paper. Gregory and Shen conjectured that b(nr) = [n/r](2) + 1 is an upper bound for the exponent of matrices in P-nr. Matrices achieving the exponent b(nr) are presented for the case when n is not a multiple of r. In particular, it is shown that b(2r+ 1,r) is the maximum exponent attained by matrices in P-2r+ 1,P-r. When n is a multiple of r, it is conjectured that the maximum exponent achieved by matrices in P-nr is strictly smaller than b(nr). Matrices attaining the conjectured maximum exponent in that set are presented. It is shown that the conjecture is true when n = 2r.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 20