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Abstract: We investigate the asymptotic behavior of the length H d (n) of a maximal chain (longest totally ordered subset) of a set of n points drawn from a uniform distribution on unit d- dimensional Eulerian cube V d = [0; 1] . For d 2, it is known that c d (n) = H d (n)=n converges in probability to a constant c d < e, with lim d!1 c d = e. For d = 2, the problem has been extensively studied, and, it is known that c 2 = 2. c d is not currently known for any d 3. We present an... (Update)
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BibTeX entry: (Update)
@article{ breimer01experimental,
author = "Eric Breimer and Mark Goldberg and Brian Kolstad and Malik Magdon-Ismail",
title = "Experimental Evaluation of the Height of a Random Set of Points in a d -Dimensional Cube",
journal = "Lecture Notes in Computer Science",
volume = "2153",
pages = "161--??",
year = "2001",
url = "citeseer.ist.psu.edu/613272.html" }
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