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<p>We highlight a certain compactness of Sidon sets and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(B_2[g]\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>B</mi> <mn>2</mn> </msub> <mrow> <mo stretchy="false">[</mo> <mi>g</mi> <mo stretchy="false">]</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>-sets and provide several applications. Notably, we prove the existence of such sets that maximize certain functions. In particular, we show the existence of a Sidon set whose reciprocal sum is equal to the distinct distance constant. We also improve the best known bounds for this constant.</p>

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Existence of a Sidon set for the distinct distance constant

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月19日

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  • Robin Riblet,
  • Titien Schehr

摘要

We highlight a certain compactness of Sidon sets and \(B_2[g]\) B 2 [ g ] -sets and provide several applications. Notably, we prove the existence of such sets that maximize certain functions. In particular, we show the existence of a Sidon set whose reciprocal sum is equal to the distinct distance constant. We also improve the best known bounds for this constant.