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Let $f:\{-1,1\}^{n}\rightarrow \{-1,1\}$ be a Boolean valued function havingtotal degree $d$. Then a conjecture due to Servedio and Gopalan asserts that$\sum_{i=1}^{n}\widehat{f}(i)\leq \sum_{j=1}^{d}\widehat{\text{Maj}}_{d}(j)$where $\text{Maj}_{d}$ is the majority function on $d$ bits. Here we give somealternative formalisms of this conjecture involving the discrete derivativeoperators on $f$.

On the Sum of Linear Coefficients of a Boolean Valued Function