Convexity, squeezing, and the Elekes-Szabó theorem

DOI10.37236/11331arXiv2205.14059MaRDI QIDQ6117405

Elaine Wong, Oliver Roche-Newton

Publication date: 19 February 2024

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.14059

zbMATH Keywords

convexitysum sets

Mathematics Subject Classification ID

Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Erd?s problems and related topics of discrete geometry (52C10) Additive bases, including sumsets (11B13) Extremal combinatorics (05D99)

Cites Work

• Polynomials vanishing on Cartesian products: the Elekes-Szabó theorem revisited
• Convexity and sumsets
• A combinatorial problem on polynomials and rational functions
• The Elekes-Szabó problem and the uniformity conjecture
• Higher convexity and iterated sum sets
• Higher convexity and iterated second moment estimates
• How to find groups?
• Constructions for the Elekes-Szabó and Elekes-Rónyai problems
• A survey of Elekes-Rónyai-type problems
• Polynomials vanishing on grids: The Elekes-Rónyai problem revisited
• On Distinct Consecutive Differences
• Sums, Products, and Dilates on Sparse Graphs
• The Uniformity Conjecture in Additive Combinatorics
• Improved Elekes-Szabó type estimates using proximity
• Growth in sumsets of higher convex functions
• Convexity, superquadratic growth, and dot products

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