2021.11.19 MATH 3600 Sum-free

187 days ago by calkin

The number $s_n$ of sum-free subsets of $[n]=\{ 1, 2, \dots n\}$ grows like 

$c 2^{n/2}$.  Subsets of odds in $[n]$ and large numbers in $[n]$ both 

give rise to about $2^{n/2}$ sets: then there is a theorem due to Ben Green, giving an upper bound of $c 2^{n/2}$ so this is the true growth rate.

How big is $c$?  Experimentally!  

Is there a parity effect (even versus odd)?

Are there constants $c_e,c_o$ so that when $n$ is respectively odd versus even, $s_n/2^{n/2} \rightarrow c_0,c_e$?