Bounds on the Number of Maximal Sum-Free Sets

We show that the number of maximal sum-free subsets of { 1 , 2 , … , n } is at most 2 3 n / 8 + o ( n ) . We also show that 2 0.406 n + o ( n ) is an upper bound on the number of maximal product-free subsets of any group of order n.