We prove that if K is a k-set of type <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$(m,q-1)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>m</mi> <mo>,</mo> <mi>q</mi> <mo>-</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$m<q-1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>m</mi> <mo><</mo> <mi>q</mi> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> in PG(3, q), then <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$(q,m,k)\in \{(2,0,1),(8,3,35),(8,3,39),(27,17,584\}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>q</mi> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>k</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <mo stretchy="false">{</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mo stretchy="false">(</mo> <mn>8</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>35</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mo stretchy="false">(</mo> <mn>8</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>39</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mo stretchy="false">(</mo> <mn>27</mn> <mo>,</mo> <mn>17</mn> <mo>,</mo> <mn>584</mn> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>.

On sets of type $(m,q-1)$ in PG(3, q)

期刊论文
发表日期：

2025年8月4日

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Mauro Zannetti,
Fulvio Zuanni

摘要

We prove that if K is a k-set of type $(m,q-1)$ $(m, q - 1)$ with $m<q-1$ $m < q - 1$ in PG(3, q), then $(q,m,k)\in \{(2,0,1),(8,3,35),(8,3,39),(27,17,584\}$ $(q, m, k) \in {(2, 0, 1), (8, 3, 35), (8, 3, 39), (27, 17, 584}$ .

On sets of type \((m,q-1)\) in PG(3, q)

摘要