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CATEGORIES:Combinatorics Seminar
SUMMARY:Shadows and intersections: stability and new proof
s - Peter Keevash (Queen Mary London)
DTSTART;TZID=Europe/London:20090514T143000
DTEND;TZID=Europe/London:20090514T153000
UID:TALK17103AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/17103
DESCRIPTION:We give a short new proof of a version of the Krus
kal-Katona theorem due to Lov\\'asz. Our method ca
n be extended to a stability result\, describing t
he approximate structure of configurations that ar
e close to being extremal\, which answers a questi
on of Mubayi. This in turn leads to another combi
natorial proof of a stability theorem for intersec
ting families\, which was originally obtained by F
riedgut using spectral\ntechniques and then sharpe
ned by Keevash and Mubayi by means of a purely com
binatorial result of Frankl. We also give an alge
braic perspective on these problems\, giving yet a
nother proof of intersection stability that\nrelie
s on expansion of a certain Cayley graph of the sy
mmetric group\, and an algebraic generalisation of
Lov\\'asz's theorem that answers a question of Fr
ankl and Tokushige.\n
LOCATION:MR12
CONTACT:Andrew Thomason
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