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SUMMARY:Minimum saturated families of sets - Matija Bucic (ETH Zurich)
DTSTART:20180503T150000Z
DTEND:20180503T160000Z
UID:TALK103615@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:A family F of subsets of [n] is called s-saturated if it conta
 ins no s pairwise disjoint sets\, and moreover\, no set can be added to F 
 while preserving this property. More than 40 years ago\, Erdős and Kleitm
 an conjectured that an s-saturated family of subsets of [n] has size at le
 ast (1 - 2^-(s-1)^)2^n^. It is easy to show that every s-saturated family 
 has size at least 2^n-1^\, but\, as was mentioned by Frankl and Tokushige\
 , even obtaining a slightly better bound of (1/2 + ε)2^n^\, for some fixe
 d ε > 0\, seems difficult. We prove such a result\, showing that every s-
 saturated family of subsets of [n] has size at least (1 - 1/s)2^n^. This i
 s joint work with S.  Letzter\, B. Sudakov and T. Tran.\n
LOCATION:MR12
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