平行自由构形

Parallel Free Arrangements

自由构形是超平面构形中一类重要的构形.本文将自由构形进行了推广,用平行的超平面组代替自由构形中的单个超平面,进而得到了一类新的超平面构形-平行自由构形,并运用Whitney定理求出了其特征多项式及区域个数,推广了n维向量空间中自由构形的相关结论.

Free arrangement is a very important kind of hyperplane arrangement. In this paper,we define a new kind of hyperplane arrangement, using parallel hyperplane groups instead of single＇ s hyperplane of free arrangement. And we extract the characteristic polynomial and the number of the areas of this new kind of hyperplane arrangements in n-dimensional vector space using the Whitney theorem, which popularize the related conclusion of the n free arrangements in n-dimensional vector space.