Hong Liu (UIC): The number of maximal sum-free subsets of integers |
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Péntek, 25. Július 2014, 11:00 - 11:45
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Abstract. Cameron and Erdős raised the question of how many \emph{maximal} sum-free sets there are in $\{1, dots , n\}$, giving a lower bound of $2^{\lfloor n/4 \rfloor }$. In this paper we prove that there are in fact at most $2^{(1/4+o(1))n}$ maximal sum-free sets in $\{1,dots , n\}$.
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. |
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Hely : Bolyai Intézet, Aradi Vértanúk tere, Szőkefalvi-Nagy szoba |
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