论文标题
盒子中的细胞和超平面
Cells in the box and a hyperplane
论文作者
论文摘要
众所周知，一条线最多可以与$ n \ times n $棋盘的$ 2N-1 $单元相交。在这里，我们考虑了高维版本：$ d $ d $ n \ times \ ldots \ times n $ box的$ d $ d $ d $ d $ n $ box中有多少个单元格可以相交？我们还证明了以下众所周知的事实的晶格类似物。如果$ k，l $是$ r^d $和$ k \ subset l $的凸体，则$ k $的表面积小于$ l $。
It is well-known that a line can intersect at most $2n-1$ cells of the $n \times n$ chessboard. Here we consider the high dimensional version: how many cells of the $d$-dimensional $n\times \ldots \times n$ box can a hyperplane intersect? We also prove the lattice analogue of the following well-known fact. If $K,L$ are convex bodies in $R^d$ and $K\subset L$, then the surface area of $K$ is smaller than that of $L$.
