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<p>We show an improved quantitative lower bound for the size of the sumsets of sets containing no non-trivial <i>k</i>-term arithmetic progressions for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1157_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(k\ge 4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>≥</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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A note on sumsets of progression-free sets

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月1日

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  • Tomasz Schoen

摘要

We show an improved quantitative lower bound for the size of the sumsets of sets containing no non-trivial k-term arithmetic progressions for \(k\ge 4\) k ≥ 4 .