The Characteristic Polynomial And The Number Of The Area Of Some Kinds Of Hyperplane Arrangement

In this paper,we calculate the charicteristic polynomial and the number of the areas of some kinds of hyperplane arrangement. FreeFirst we define a new kind of hyperplane arrangement-parallel free arrangement,which maintains the restriction "in general positions". And we calculate the characteristic polynomial and the number of the areas of this new kind of hyperplane arrangement in n-dimensional vector space using the Whitney theorem, which popularize the related conclusion o f the n free arrangement in n-dimensional vector space.And we also defined another new kind of hyperplane arrangement-species free arrangement, calculat-ing the characteristic polynomial and the number of the areas of the species arrangement in n-dimensional vector space using the Whitney theorem, and popularized the related conclusion of the parallel free arrange-ment in n-dimensional vector space.And we calculate the characteristic polynomial and the number of the areas of the Shi arrangement and the Catalan arrangement and the extracted arrangements of these two arrangements in the lower dimensional vector space by the thereams of the finite field.