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CATEGORIES:Combinatorics Seminar
SUMMARY:The number of maximal sum-free subsets of integers
- Andrew Treglown (University of Birmingham)
DTSTART;TZID=Europe/London:20141127T143000
DTEND;TZID=Europe/London:20141127T153000
UID:TALK55196AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/55196
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 Sapo
zhenko proved that there are O(2^{n/2}) sum-free s
ets in {1\,...\,n}\, thereby resolving a conjectur
e of Cameron and Erdős.\n\nCameron and Erdős also
raised the question of how many maximal sum-free s
ets there are in {1\,...\,n}\, giving a lower boun
d 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 contai
ner and removal lemmas of Green as well as a resul
t of Deshouillers\, Freiman\, Sós and Temkin on th
e structure of sum-free sets. This is joint work w
ith József Balogh\, Hong Liu and Maryam\nSharifzad
eh.\n
LOCATION:MR12
CONTACT:Andrew Thomason
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