2000 character limit reached
A new bound for the Fourier-Entropy-Influence conjecture (2312.08271v1)
Published 13 Dec 2023 in math.CO and math.FA
Abstract: In this paper, we prove that the Fourier entropy of an $n$-dimensional boolean function $f$ can be upper-bounded by $O(I(f)+ \sum\limits_{k\in[n]}I_k(f)\log \frac{1}{I_k(f)})$, where $I(f)$ is its total influence and $I_k(f)$ is the influence of the $k$-th coordinate. The proof is elementary and uses iterative bounds on moments of Fourier coefficients over different levels.
Sponsor
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.