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CATEGORIES:Combinatorics and Probability Seminar
SUMMARY:An isoperimetric approach to some Erdos-Ko-Rado ty
pe problems - David Ellis (QMUL)
DTSTART:20181009T140000Z
DTEND:20181009T150000Z
UID:TALK3279AT
URL:/talk/index/3279
DESCRIPTION:An Erdos-Ko-Rado (EKR) problem asks for a determin
ation of the maximum possible size of a family of
sets\, subject to some intersection requirement on
the sets in the family. An EKR 'stability' proble
m asks for a description of the families that sati
sfy this intersection requirement and moreover hav
e size 'close' to the maximum possible size. We ma
ke some progress on various EKR problems and EKR s
tability problems\, via a technique based on isope
rimetric inequalities for subsets of the hypercube
. We substantially improve an old result of Frankl
and Furedi on the maximum possible size of the un
ion of a fixed number of intersecting families of
k-element subsets of an n-element set\, resolving
the question for k < (1/2-o(1))n\, and we prove an
almost-sharp 'stability' result on t-intersecting
families of k-element sets\, strengthening a resu
lt of Friedgut. Based on joint work with Nathan Ke
ller (Bar Ilan University) and Noam Lifshitz (Bar
Ilan University).
LOCATION:Arts LR2
CONTACT:Guillem Perarnau
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