Entropy and set cardinality inequalities for partition-determined functions

DOI10.1002/rsa.20385zbMath1244.05024arXiv0901.0055OpenAlexW3106140828MaRDI QIDQ2904591

Mokshay Madiman, Prasad Tetali, Adam W. Marcus

Publication date: 14 August 2012

Published in: Random Structures & Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.0055

zbMATH Keywords

sumsetsentropy inequalitiesadditive combinatoricscardinality inequalities

Mathematics Subject Classification ID

Partitions of sets (05A18) Measures of information, entropy (94A17) Additive bases, including sumsets (11B13)

Related Items (12)

Log-concavity, ultra-log-concavity, and a maximum entropy property of discrete compound Poisson measures ⋮ Volumes of subset Minkowski sums and the Lyusternik region ⋮ Computing from projections of random points ⋮ Deletion correcting codes meet the Littlewood-Offord problem ⋮ Notes on use of generalized entropies in counting ⋮ The convexification effect of Minkowski summation ⋮ The cardinality of sumsets: different summands ⋮ Entropy versions of additive inequalities ⋮ On self-similar sets with overlaps and inverse theorems for entropy ⋮ Majorization and Rényi entropy inequalities via Sperner theory ⋮ Additive Combinatorics: With a View Towards Computer Science and Cryptography—An Exposition ⋮ Entropy Inequalities for Sums in Prime Cyclic Groups

Cites Work

• Reverse Brunn-Minkowski and reverse entropy power inequalities for convex measures
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• Compressions and isoperimetric inequalities
• Random walks on discrete groups: Boundary and entropy
• Some intersection theorems for ordered sets and graphs
• Two Constructions on Limits of Entropy Functions
• Generalized Entropy Power Inequalities and Monotonicity Properties of Information
• Hypergraphs, Entropy, and Inequalities
• Sumsets and entropy
• Nonnegative entropy measures of multivariate symmetric correlations
• Polymatroidal dependence structure of a set of random variables
• Projections of Bodies and Hereditary Properties of Hypergraphs
• Sumset and Inverse Sumset Theory for Shannon Entropy
• Information Inequalities for Joint Distributions, With Interpretations and Applications
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