Exponents of classes of non-negative matrices

V.N. Sachkov and I.B. Oshkin

Abstract

A square non-negative matrix is called primitive if all the elements of some power of this matrix are positive. The exponent of a primitive matrix is the minimum power satisfying this condition. The exponent of a class of primitive matrices is the minimum power such that all the matrices of the class to this power have positive elements only. In this paper, bounds for the exponents of primitive matrices and classes of matrices are obtained.

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Discrete Mathematics and Applications provides the latest information on the development of discrete mathematics in Russia to a world-wide readership. The journal covers various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.

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