abs_vol20_pp640-660. 8KB Jun 04 2011 12:05:48 AM

ELA

ON THE GAPS IN THE SET OF EXPONENTS OF BOOLEAN

PRIMITIVE CIRCULANT MATRICES

∗

MARIBEL I. BUENO†_{ANDSUSANA FURTADO}‡

Abstract. In this paper, we consider the problem of describing the possible exponents of boolean primitive

circulant matrices. We give a conjecture for the possible such exponents and prove this conjecture in several cases. In particular, we consider in greater detail the case of matrices whose generating vector has three nonzero entries.

Key words. Circulant primitive matrices, Exponent of primitive matrices, Circulant digraphs, Basis for a group. AMS subject classifications. 11P70, 05C25, 05C50.

∗_{Received by the editors December 7, 2009. Accepted for publication August 22, 2010. Handling Editor: Bryan}

L. Shader.

†_{Department of Mathematics, University of California, Santa Barbara, CA, USA (mbueno@math.ucsb.edu).}

Supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under grant MTM2009-09281.

‡_{Faculdade de Economia do Porto, Rua Dr. Roberto Frias, 4200-464 Porto, Portugal (sbf@fep.up.pt).}

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 20, pp. 640-660, October 2010