Given a Boolean function f: \{-1,1\}^n\rightarrow \{-1,1\}, define the Fourier distribution to be the distribution on subsets of [n], where each S\subseteq [n] is sampled with probability \widehat{f}(S)^2. The Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai [FK96] seeks to relate two fundamental measures associated with the Fourier distribution: does ... more >>>

We describe a new construction of Boolean functions. A specific instance of our construction provides a 30-variable Boolean function having min-entropy/influence ratio to be 128/45 ? 2.8444 which is presently the highest known value of this ratio that is achieved by any Boolean function. Correspondingly, 128/45 is also presently the ... more >>>