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<p>We prove that if <i>K</i> is a set of type <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="22_2025_760_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="68" /> </InlineMediaObject> <EquationSource Format="TEX">\((q+3,n)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>q</mi> <mo>+</mo> <mn>3</mn> <mo>,</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="22_2025_760_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">\(n&gt;q+3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>&gt;</mo> <mi>q</mi> <mo>+</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation> in <i>PG</i>(3,&#xa0;<i>q</i>), then <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="22_2025_760_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="78" /> </InlineMediaObject> <EquationSource Format="TEX">\(n=2q+3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>2</mn> <mi>q</mi> <mo>+</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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On sets of type \((q+3,n)\) in PG(3, q)

  • 期刊论文

  • 发表日期：

    2025年7月5日

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  • Fulvio Zuanni

摘要

We prove that if K is a set of type \((q+3,n)\) ( q + 3 , n ) with \(n>q+3\) n > q + 3 in PG(3, q), then \(n=2q+3\) n = 2 q + 3 .