Title

The longest chain among random points in euclidean space

Abstract

Let n random points be chosen independently from the uniform distribution on the unit k-cube [0, 1]k. Order the points coordinate-wise and let Hk(n) be the cardinality of the largest chain in the resulting partially ordered set. We show that there are constants C1, C2,… such that ck

Publication Title

Proceedings of the American Mathematical Society

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