Counting generalized sum-free sets (Q1379641)

Let \(k\), \(l\), \(n\) be nonnegative integers such that \(k\geq 4l- 1\). The authors show that the number of subsets of \(\{1,\dots, n\}\) which have no solutions to the equation \[ x_1+ x_2+\cdots+ x_k= x_1+ x_2+\cdots+ x_l \] is at most \(c2^{(k- 1)n/k}\).