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A Useful Inequality for the Binary Entropy Function

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arxiv 2301.09664 v1 pith:3APCTDA3 submitted 2023-01-23 math.CO cs.CCcs.ITmath.IT

Ravi B. Boppana (MIT) This is my paper · ORCID
classification math.COcs.CCcs.ITmath.IT
keywords inequalityentropyusedbinaryfunctionproofachievebasic
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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.

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  1. Entropy methods in combinatorics

    math.CO 2026-07 accept novelty 2.0 of 10

    A selective survey of entropy methods in combinatorics, detailing randomized chain rules, Shearer's inequality, random homomorphisms, Pinsker-type arguments, the union-closed sets breakthrough, and entropy approaches ...

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