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On the structure of large sum-free sets of integers
- 1.0484274 - ÚI 2019 RIV IL eng J - Journal Article
Tran, Tuan
On the structure of large sum-free sets of integers.
Israel Journal of Mathematics. Roč. 228, č. 1 (2018), s. 249-292. ISSN 0021-2172. E-ISSN 1565-8511
R&D Projects: GA ČR GJ16-07822Y
Institutional support: RVO:67985807
Keywords : sum-free sets * structure * stability * counting * hypergraph containers
OECD category: Pure mathematics
Impact factor: 0.764, year: 2018
A set of integers is called sum-free if it contains no triple (x,y,z) of not necessarily distinct elements with x+y=z. In this note we provide a structural characterisation of sum-free subsets of {1,2,...,n} of density at least 2/5-c, where c is an absolute positive constant. As an application we derive a stability version of Hu's theorem [Proc. Amer. Math. Soc. 80 (1980), 711-712] about the maximum size of a union of two sum-free sets in {1,2,...,n}. We then use this result to show that the number of subsets of {1,2,...,n} which can be partitioned into two sum-free sets is O(2^{4n/5}), confirming a conjecture of Hancock, Staden and Treglown.
Permanent Link: http://hdl.handle.net/11104/0279675
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