This paper is concerned with five kinds of modification of hyperplane arrangements, including elementary lift, parallel translation, coning, one-element extension and restriction to a hyperplane. We show that the combinatorial classification of all hyperplane arrangements of each kind of modification will be characterized by the intersection lattice of the discriminantal or adjoint arrangement. Based on the classifications, a number of combinatorial invariants, including the unsigned coefficients of the Whitney polynomial, Whitney numbers of both kinds, face numbers and region numbers, are constants on those strata associated to the intersection lattice of the discriminantal or adjoint arrangement. Moreover, we further establish the order-preserving relations of those combinatorial invariants and a series of convolution formulae on the characteristic polynomials.

本文涉及超平面排列的五种修改，包括基本升力、平行平移、圆锥、单元素扩展和超平面限制。我们证明了每种修改的所有超平面排列的组合分类将由相交格来表征判别式或伴随式安排。基于分类，许多组合不变量，包括惠特尼多项式的无符号系数、两种类型的惠特尼数、面数和区域数，是与判别或伴随排列的交点格相关的那些层上的常数。此外，我们进一步建立了这些组合不变量的保序关系和一系列特征多项式的卷积公式。