Recently, Eisenbrand, Pach, Rothvo?, and Sopher studied the function $M(m, n)$, which is the largest cardinality of a convexly independent subset of the Minkowski sum of some planar point sets $P$ and $Q$ with $|P| = m$ and $|Q| = n$. They proved that $M(m,n)=O(m^{2/3}n^{2/3}+m+n)$, and asked whether a superlinear lower bound exists for $M(n,n)$. In this note, we show that their upper bound is the best possible apart from constant factors.
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机译：最近，Eisenbrand，Pach，Rothvo？和Sopher研究了函数$ M（m，n）$，这是一些平面点集$ P $和$ Q $的Minkowski和的凸独立子集的最大基数，其中$ | P | = m $和$ | Q | = n $。他们证明$ M（m，n）= O（m ^ {2/3} n ^ {2/3} + m + n）$，并询问$ M（n，n）是否存在超线性下界$。在此注释中，我们显示了除恒定因素外，它们的上限是最好的。
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