A Useful Inequality for the Binary Entropy Function
Combinatorics
2023-01-25 v1 Computational Complexity
Information Theory
math.IT
Abstract
We provide a simple proof of a curious inequality for the binary entropy function, an inequality that has been used in two different contexts. In the 1980's, Boppana used this entropy inequality to prove lower bounds on Boolean formulas. More recently, the inequality was used to achieve major progress on Frankl's union-closed sets conjecture. Our proof of the entropy inequality uses basic differential calculus.
Keywords
Cite
@article{arxiv.2301.09664,
title = {A Useful Inequality for the Binary Entropy Function},
author = {Ravi B. Boppana},
journal= {arXiv preprint arXiv:2301.09664},
year = {2023}
}
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4 pages