On the Analysis of Boolean Functions and Fourier-Entropy-Influence Conjecture

2023/08/01 by Han, Xiao
#Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2308.00509

Abstract

This manuscript includes some classical results we select apart from the new results we've found on the Analysis of Boolean Functions and Fourier-Entropy-Influence conjecture. We try to ensure the self-completeness of this work so that readers could probably read it independently. Among the new results, what is the most remarkable is that we prove that the entropy of a boolean function f could be upper bounded by O(I(f))+O(∑_kI_k(f)log (1/I_k(f))).

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