English

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

Combinatorics 2023-11-21 v3 Functional Analysis

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 ff could be upper bounded by O(I(f))+O(kIk(f)log(1/Ik(f)))O(I(f))+O(\sum\limits_{k}I_k(f)\log (1/I_k(f))).

Keywords

Cite

@article{arxiv.2308.00509,
  title  = {On the Analysis of Boolean Functions and Fourier-Entropy-Influence Conjecture},
  author = {Xiao Han},
  journal= {arXiv preprint arXiv:2308.00509},
  year   = {2023}
}