The longest chain among random points in Euclidean space

Authors:
Béla Bollobás and Peter Winkler

Journal:
Proc. Amer. Math. Soc. **103** (1988), 347-353

MSC:
Primary 60C05; Secondary 06A10, 11K99

DOI:
https://doi.org/10.1090/S0002-9939-1988-0943043-6

MathSciNet review:
943043

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Abstract | References | Similar Articles | Additional Information

Abstract: Let random points be chosen independently from the uniform distribution on the unit -cube . Order the points coordinate-wise and let be the cardinality of the largest chain in the resulting partially ordered set.

We show that there are constants such that , and in probability. This generalizes results of Hammersley, Kingman and others on Ulam's ascending subsequence problem, and settles a conjecture of Steele.

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DOI:
https://doi.org/10.1090/S0002-9939-1988-0943043-6

Article copyright:
© Copyright 1988
American Mathematical Society