In 1996, Friedgut and Kalai made the Fourier Entropy–Influence Conjecture: For every Boolean function f : {−1, 1} → {−1, 1} it holds that H[f̂] ≤ C · I[f ], where H[f̂] is the spectral entropy of f , I[f ] is the total influence of f , and C is a universal constant. In this work we verify the conjecture for symmetric functions. More generally, we verify it for functions with symmetry group Sn1×· ...
