The complexity of depth-3 circuits computing symmetric Boolean functions

We give tight lower bounds for the size of depth-3 circuits with limited bottom fanin computing symmetric Boolean functions. We show that any depth-3 circuit with bottom fanin k which computes the Boolean function , has at least n(1+1/k)/(n+1) gates. We show that for this lower bound is essentially tight, by generalizing a known upper bound on the size of depth-3 circuits with bottom fanin 2, computing symmetric Boolean functions.