On the exponent of r-regular primitive matrices

• Type: Article in International Scientific Journal
• Date: 2008

Authors

Maria Isabel Bueno (Author) Other; Susana Borges Furtado (Author) FEP

Journal

Title: Electronic Journal of Linear Algebra

Vol. 17

Pages: 28-47

ISSN: 1537-9582

Publisher: INT LINEAR ALGEBRA SOC

Indexing

ISI Web of Knowledge - 4 Citations

ISI Web of Science

Scopus - 4 Citations

Scientific classification

FOS: Natural sciences

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 20