Longest k-monotone chains
Metric Geometry
2020-09-30 v1 Probability
Abstract
We study higher order convexity properties of random point sets in the unit square. Given uniform i.i.d random points, we derive asymptotic estimates for the maximal number of them which are in -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 (longest increasing sequences) and (longest convex chains).
Keywords
Cite
@article{arxiv.2009.13887,
title = {Longest k-monotone chains},
author = {Gergely Ambrus},
journal= {arXiv preprint arXiv:2009.13887},
year = {2020}
}