乘积构形的良划分性

Nice partition of product arrangements

已知乘积构形为超可解构形充要条件是每个因子构形都是超可解构形,将此结论推广到良划分构形,证明了乘积构形(A1×…×Ak,V1…Vk)为良划分构形的充要条件是因子构形(Ai,Vi),1≤i≤k都是良划分构形。

It is known that a product arrangement is a supersolvable arrangement if, and only if, each factor arrangement is also a supersolvable arrangement. This conclusion for supersolvable arrangements is extended to nice partition arrangements and it is proven that a product arrangement （At,×…×Ak;V1＋…＋VK） is a nice partition arrangement if, and only if, each factor arrangement （Ai, Vi） , 1 ≤ i ≤ k is also a nice partition arrangement.