On random sections of the cube

Details On random sections of the cube On random sections of the cube

1998-12-21

arxiv.org/abs/math/9812123v1

Mathematics

Probability

17 pages; To appear in "Computational and Discrete Geometry"

Scientific paper

Let $f(j,k,n)$ denote the expected number of $j$-faces of a random
$k$-section of the $n$-cube. A formula for $f(0,k,n)$ is presented, and for
$j\geq 1$, a lower bound for $f(j,k,n)$ is derived, which implies a precise
asymptotic formula for $f(n-m,n-l,n)$ when $1\leq l$n\to\8$.

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