| Mittagsseminar Talk Information | |
Date and Time: Tuesday, July 27, 2004, 12:15 pm Duration: This information is not available in the database Location: This information is not available in the database Speaker: Volker Kaibel (TU Berlin) Low-dimensional faces of random 0/1-polytopesLet P be a random 0/1-polytope in Rd with n(d) vertices, and
denote by φk(P) the k-face density of P, i.e.,
the quotient of the number of k-dimensional faces of P and
\binom{n(d)}{k+1}. For each k >= 2, we establish the existence
of a sharp threshold for the k-face density and determine the
values of the threshold numbers τk such that, for all
ε > 0,
E(φk(P)) =
- 1- o(1), if n(d)<= 2(τk-ε)d for all d
- o(1), if n(d)>= 2(τk+ε)d for all d
holds for the expected value of φk(P). The threshold for
k=1 has recently been determined by K. and Remshagen (2003).
In particular, these results indicate that the high face densities
often encountered in polyhedral combinatorics (e.g., for the
cut-polytopes of complete graphs) should be considered more as a
phenomenon of the general geometry of 0/1-polytopes than as a
feature of the special combinatorics of the underlying problems.
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