Distribution of the exponents of primitive circulant matrices in the first four boxes of ¿n

• Tipo: Artigo em Revista Científica Internacional
• Data: 2012

Autores

Bueno, MI (Autor) Outra; Fang, KY (Autor) Outra; Fuller, S (Autor) Outra; Susana Borges Furtado (Autor) FEP

Revista

Título: Involve

Vol. 5 Nº 2

Páginas: 187-205

ISSN: 1944-4176

Editora: Mathematical Sciences Publishers

Indexação

Scopus - 0 Citações

Outras Informações

ID Authenticus: P-00W-Z8J

DOI: 10.2140/involve.2012.5.187

Abstract (EN): We consider the problem of describing the possible exponents of n-by-n boolean primitive circulant matrices. It is well known that this set is a subset of [1, n ¿1] and not all integers in [1, n ¿1] are attainable exponents. In the literature, some attention has been paid to the gaps in the set of exponents. The first three gaps have been proven, that is, the integers in the intervals [n2+1, n¿2], [n3+2, n2¿2] and [n4+3, n ¿2] are not attainable exponents. Here we study the distribution 3 of exponents in between those gaps by giving the exact exponents attained there by primitive circulant matrices. We also study the distribution of exponents in between the third gap and our conjectured fourth gap. It is interesting to point out that the exponents attained in between the (i ¿1)-th and the i-th gap depend on the value of n mod i. © 2012, Mathematical Sciences Publishers.

Idioma: Inglês

Tipo (Avaliação Docente): Científica