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arXiv · 2009.13887

Longest k-monotone chains

Gergely Ambrus
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Abstract

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).

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Gergely Ambrus. 2020-09-29. Longest k-monotone chains. https://arxiv.org/abs/2009.13887

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