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<p>This paper considers some different measures for how additively structured a convex set can be. The main result gives a construction of a convex set <i>A</i> containing <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Omega (|A|^{3/2})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">(</mo> <mo stretchy="false">|</mo> <mi>A</mi> <msup> <mo stretchy="false">|</mo> <mrow> <mn>3</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> three-term arithmetic progressions.</p>

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Additive Structure in Convex Sets

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月28日

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  • Thomas F. Bloom,
  • Jakob Führer,
  • Oliver Roche-Newton

摘要

This paper considers some different measures for how additively structured a convex set can be. The main result gives a construction of a convex set A containing \(\Omega (|A|^{3/2})\) Ω ( | A | 3 / 2 ) three-term arithmetic progressions.