论文标题
最长的K-单酮链
Longest k-monotone chains
论文作者
论文摘要
我们研究单位正方形中随机点集的高阶凸度性能。给定$ n $统一的i.i.d随机点，我们得出了$ k $ - 单酮位置的最大数量的渐近估计值，但受到轻度边界条件的约束。除了确定预期的数量级外，我们还证明了强烈的浓度估计值。我们提供一个通用框架，其中包括先前研究的$ k = 1 $（最长增加序列）和$ k = 2 $（最长的凸链）的案例。
We study higher order convexity properties of random point sets in the unit square. Given $n$ uniform i.i.d random points, we derive asymptotic estimates for the maximal number of them which are in $k$-monotone position, subject to mild boundary conditions. Besides determining the order of magnitude of the expectation, we also prove strong concentration estimates. We provide a general framework that includes the previously studied cases of $k=1$ (longest increasing sequences) and $k=2$ (longest convex chains).
