Sumset and Inverse Sumset Theory for Shannon Entropy

DOI10.1017/S0963548309990642zbMath1239.11015arXiv0906.4387OpenAlexW3103598778MaRDI QIDQ4933603

Terence C. Tao

Publication date: 14 October 2010

Published in: Combinatorics, Probability and Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.4387

zbMATH Keywords

entropysumsetadditive combinatorics

Mathematics Subject Classification ID

Measures of information, entropy (94A17) Additive bases, including sumsets (11B13) Representation functions (11B34)

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Cites Work

• John-type theorems for generalized arithmetic progressions and iterated sumsets
• A new proof of Szemerédi's theorem for arithmetic progressions of length four
• A statistical theorem of set addition
• Product set estimates for non-commutative groups
• Solution of Shannon’s problem on the monotonicity of entropy
• Freiman's theorem in an arbitrary abelian group