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 >>>

We show that the ''majority is least stable'' conjecture is true for $n=1$ and $3$ and false for all odd $n\geq 5$.

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The influence of a set of variables on a Boolean function has three separate definitions in the literature, the first due to Ben-Or and Linial (1989), the second due to Fischer et al. (2002) and Blais (2009) and the third due to Tal (2017). The goal of the present work ... more >>>