On the structure of large sum-free sets of integers

0484274 - ÚI 2019 RIV IL eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR GJ16-07822Y
Institucionální podpora: RVO:67985807
Klíčová slova: sum-free sets * structure * stability * counting * hypergraph containers
Obor OECD: Pure mathematics
Impakt faktor: 0.764, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0279675