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

• Type: Article in International Scientific Journal
• Date: 2012

Authors

Bueno, MI (Author) Other; Fang, KY (Author) Other; Fuller, S (Author) Other; Susana Borges Furtado (Author) FEP

Journal

Title: Involve

Vol. 5 No. 2

Pages: 187-205

ISSN: 1944-4176

Publisher: Mathematical Sciences Publishers

Indexing

Scopus - 0 Citations

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific