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DESCRIPTION: Doignon proved a discrete version of Helly's theorem claiming
that a finite family of convex sets in R^n intersects in an integral point
if every subfamily of size at most 2^n does so. Motivated by applications i
n integer programming\, Aliev et al. recently obtained a quantitative versi
on of this result\, which guarantees that a finite family of convex sets in
tersects in k integral points whenever every subfamily of size at most c_n(
k) does so. The best current upper bound on the minimal such constant c_n(k
) grows linearly with the parameter k. Based on a connection to the number
of boundary integral points in strictly convex sets\, we show that the asym
ptotic behavior of c_n(k) is sublinear in dimension two and we determine th
e exact value of c_n(k) for k at most four. ------
DTSTAMP:20151208T180200
DTSTART:20151210T141500
CLASS:PUBLIC
LOCATION:Seminar Room\, Arnimallee 2\, FU Berlin
SEQUENCE:0
SUMMARY:Discrete Geometry Seminar- Matthias Henze
UID:57275367@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/math/groups/discgeom/dates/olderdates/Discr
ete-Geometry-Seminar-Henze2.html
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