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    Title      l  THE NUMBER OF B3-SETS OF A GIVEN CARDINALITY
    Author   l  DOMINGOS DELLAMONICA JR., YOSHIHARU KOHAYAKAWA, SANG JUNE LEE, VOJTECH RODL, AND WOJCIECH SAMOTIJ
    Date   l  2014-02-10
    Category   l  ASARC-Preprint-14-04
    Download    l 1391992452_0.225315.pdf  
Abstract:

A set~$S$ of integers is a emph{$B_3$-set} if all the sums of the form~$a_1+a_2+a_3$, with $a_1$, $a_2$ and~$a_3in S$ and~$a_1leq a_2leq a_3$, are distinct. We obtain asymptotic bounds for the number of $B_3$-sets of a given cardinality contained in the interval $[n]={1,dots,n}$. We use these results to estimate the maximum size of a $B_3$-set contained in a typical (random) subset of~$[n]$ of a given cardinality. These results confirm conjectures recently put forward by the authors [emph{On the number of $B_h$-sets}, submitted].

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