论文标题
各种尺寸的定向正方形之间可以存在多少个接触？
How many contacts can exist between oriented squares of various sizes?
论文作者
论文摘要
正方形的同一个平方是任何一组各种大小的正方形，其方向相同，没有两个正方形具有重叠的内部。如果所有$ n $ squares的大小相同，那么我们可以通过在网格编队中安排正方形来达到大约$ 4N $的联系。一组$ n $正方形的最大接触数量将大幅下降，但是，如果随机选择每个正方形的大小，则可以随机选择每个正方形的大小。在以下论文中，我们描述了确定一组固定尺寸的$ n $正方形的必要条件，可以将其布置到具有超过$ 2N-2 $触点的同种座式正方形包装中。然后，我们证明，如果平方的各种宽度不满足有限的线性方程式，则$ n $正方形的任何（可能不是同型）包装最多都将具有$ 2N-2 $面对面的联系。
A homothetic packing of squares is any set of various-size squares with the same orientation where no two squares have overlapping interiors. If all $n$ squares have the same size then we can have up to roughly $4n$ contacts by arranging the squares in a grid formation. The maximum possible number of contacts for a set of $n$ squares will drop drastically, however, if the size of each square is chosen more-or-less randomly. In the following paper we describe a necessary and sufficient condition for determining if a set of $n$ squares with fixed sizes can be arranged into a homothetic square packing with more than $2n-2$ contacts. Using this, we then prove that any (possibly not homothetic) packing of $n$ squares will have at most $2n-2$ face-to-face contacts if the various widths of the squares do not satisfy a finite set of linear equations.
