本原不可幂符号矩阵的完全不可分基指数
Fully Indecomposable Bases of Primitive Non-Powerful Sign Pattern Matrices

将可分性的概念推广至广义符号方阵中,定义了完全模糊不可分和部分模糊可分的广义符号方阵;把本原(0,1)方阵的(严格)完全不可分指数的概念推广到本原不可幂(广义)符号方阵,提出了(严格)完全不可分基指数的概念并给出了相应的图论刻画,同时获得了若干本原不可幂符号矩阵类的(严格)完全不可分基指数的上界. 进一步地,将完全模糊不可分广义符号矩阵和(严格)完全不可分基指数的概念分别拓展为w-模糊不可分广义符号矩阵和(严格)w-不可分基指数.
： The definition of indecomposability for generalized sign pattern matrices is extended firstly in this paper. The fully ambiguous indecomposable generalized sign pattern matrices and partly ambiguous decomposable generalized sign pattern matrices are then defined. Moreover, the (strict) fully indecomposable base for a primitive non-powerful (generalized) sign pattern matrix is put forward, which is the generalization of the (strict) fully indecomposable exponent for a primitive (0,1) matrix. Meanwhile, the graph depicts for (strict) indecomposable base is given, and some upper bounds for the (strict) fully indecomposable base of primitive non-powerful sign pattern matrices are obtained. Furthermore, the definitions of fully ambiguous indecomposable generalized sign pattern matrix and (strict) fully indecomposable base to w-ambiguous indecomposable generalized sign pattern matrix and (strict) w-indecomposable based are generalized respectively