Entropy influence conjecture

In mathematics, the entropy influence conjecture is a statement about Boolean functions originally conjectured by Ehud Friedgut and Gil Kalai in 1996.
Statement.
For a function formula_1 note its Fourier expansion
The entropy–influence conjecture states that there exists an absolute constant "C" such that formula_3 where the total influence formula_4 is defined by
and the entropy formula_6 (of the spectrum) is defined by 
(where "x" log "x" is taken to be 0 when "x" = 0).
See also.
Analysis of Boolean functions