论文标题
最小瓷砖特性的最大瓷砖
Maximum tilings with the minimal tile property
论文作者
论文摘要
如果最小的瓷砖可以瓷砖所有其他瓷砖，则单位正方形的平铺是MTP瓷砖。我们查看函数$ f（n）= \ max \ sum s_i $，其中$ s_i $是$ i $ th tile的侧面长度，然后将总和乘以所有MTP Tilings带有$ n $ tiles。如果$ n = k^2+3 $，则认为$ f（k^2+3）= k+1/k $。我们表明，任何违反猜想的瓷砖都必须由至少三个瓷砖尺寸组成，并且完全具有最小的瓷砖。
A tiling of the unit square is an MTP tiling if the smallest tile can tile all the other tiles. We look at the function $f(n)=\max \sum s_i$, where $s_i$ is the side length of the $i$th tile and the sum is taken over all MTP tilings with $n$ tiles. If $n=k^2+3$, it was conjectured that $f(k^2+3)=k+1/k$. We show that any tiling that violates the conjecture must consist of at least three tile sizes and has exactly one minimal tile.
