关于矩形平移的Helly数

On the Helly Number for Translates of a Rectangle

证明了对于平面上由两两不交的矩形的平移形成的集簇 ,其Helly数等于 5 ;对于Rd 中由 (d-2 )分离的超矩形的平移形成的集簇 ,其Helly数大于等于d+3 ,其中d≥ 3 .

Prove that for the family of pairwise disjoint translates of a rectangle in the plane,the Helly number is equal to 5.For the family of ( d -2) separated translates of a hyperrectangle in R d ,the Helly number is greater or equal to d +3.