围长为2的本原无限布尔方阵类的本原指数集

On primitive exponent set for the class of primitive infinite Boolean matrices with girth 2

研究了围长为2的无限布尔方阵的本原性,通过无限有向图D(A)的直径给出了这类矩阵的本原指数的上确界,最后证明了直径小于等于d且围长为2的本原无限布尔方阵所构成的矩阵类的本原指数集为Ed0={2,3,…,3d}.

This paper studies the primitiveness of infinite Boolean matrices with girth 2. And it offers the least upper bound of the primitive exponent through the diameter of the infinite digraph D（A）.In the end we completely determine the primitive exponent set of the matrices which are class of primitive infinite Boolean matrices with girth 2 and whose diameters are not more than d is Ed^0 = {2, 3,…… , 3d}.