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SUMMARY:The number of maximal sum-free subsets of integers - Andrew Treglo
 wn (University of Birmingham)
DTSTART:20141127T143000Z
DTEND:20141127T153000Z
UID:TALK55196@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:A set S of integers is sum-free if x+y is not in S for every x
 \,y in S. Green and independently Sapozhenko proved that there are O(2^{n/
 2}) sum-free sets in {1\,...\,n}\, thereby resolving a conjecture of Camer
 on and Erdős.\n\nCameron and Erdős also raised the question of how many 
 maximal sum-free sets there are in {1\,...\,n}\, giving a lower bound of 2
 ^{n/4}. In this talk we prove that there are in fact at most 2^{(1/4+o(1))
 n} maximal sum-free sets in {1\,...\,n}. Our proof makes use of container 
 and removal lemmas of Green as well as a result of Deshouillers\, Freiman\
 , Sós and Temkin on the structure of sum-free sets. This is joint work wi
 th József Balogh\, Hong Liu and Maryam\nSharifzadeh.\n
LOCATION:MR12
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