将Moser平方Packing问题化为有界平方数
Reducing Moser's Square Packing Problem to a Bounded Number of Squares
摘要：
广为人知的莫泽正方形填充问题要求最小面积$A$，使得对于总面积为$1$的正方形的任何集合$S$，存在面积为$A$的矩形$R$，其中$S$中的正方形允许内部不相交的轴平行填充。它是由莫泽在1966年提出的，至今仍未解决。$\frac{2+\sqrt{3}}{3}\leq A$最著名的下限是由Novotnatrium提出的，并且Platz已经证明对于高达$11$平方是足够的，而Hougardy和Ilhan已经建立了$A < 1.37$。在本文中，我们减少莫泽的广场包装问题的一个有限的广场上的问题在以下意义上：我们展示了如何计算一个自然数$N$，使得它是足够的，以确定$A$的值为集合包含最多$N$广场的总面积$1$。
英文摘要：
The problem widely known as Moser's Square Packing Problem asks for the smallest area $A$ such that for any set $S$ of squares of total area $1$, there exists a rectangle $R$ of area $A$ into which the squares in $S$ permit an internally-disjoint, axis-parallel packing. It was formulated by Moser in 1966 and remains unsolved so far. The best known lower bound of $\frac{2+\sqrt{3}}{3}\leq A$ is due to Novotný and has been shown to be sufficient for up to $11$ squares by Platz, while Hougardy and Ilhan have established that $A < 1.37$. In this paper, we reduce Moser's Square Packing Problem to a problem on a finite set of squares in the following sense: We show how to compute a natural number $N$ such that it is enough to determine the value of $A$ for sets containing at most $N$ squares with total area $1$.
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