On the structure of large sum-free sets of integers

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F18%3A00484274" target="_blank" >RIV/67985807:_____/18:00484274 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11856-018-1763-4" target="_blank" >http://dx.doi.org/10.1007/s11856-018-1763-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11856-018-1763-4" target="_blank" >10.1007/s11856-018-1763-4</a>

Result language
angličtina
Original language name
On the structure of large sum-free sets of integers
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ16-07822Y" target="_blank" >GJ16-07822Y: Extremal graph theory and applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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