On the Height of a Random Set of Points in a $d$-Dimensional Unit Cube
Breimer, Eric ; Goldberg, Mark ; Kolstad, Brian ; Magdon-Ismail, Malik
Experiment. Math., Tome 10 (2001) no. 3, p. 583-598 / Harvested from Project Euclid
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We investigate, through numerical experiments, 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 the $d$-dimensional unit cube {\bf V}\math{_D=[0,1]^d}. For \math{d\ge2}, it is known that \math{c_d(n)=H_d(n)/n^{1/d}} converges in probability to a constant \math{c_d
Publié le : 2001-05-14
Classification:  06A07,  65C50 
@article{1069855258,
     author = {Breimer, Eric and Goldberg, Mark and Kolstad, Brian and Magdon-Ismail, Malik},
     title = {On the Height of a Random Set of Points in a $d$-Dimensional Unit Cube},
     journal = {Experiment. Math.},
     volume = {10},
     number = {3},
     year = {2001},
     pages = { 583-598},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1069855258}
}

Breimer, Eric; Goldberg, Mark; Kolstad, Brian; Magdon-Ismail, Malik. On the Height of a Random Set of Points in a $d$-Dimensional Unit Cube. Experiment. Math., Tome 10 (2001) no. 3, pp.  583-598. http://gdmltest.u-ga.fr/item/1069855258/