<p>We show that both the pseudo-embedding and pseudo-generating ranks of the projective plane <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\textrm{PG}(2,8)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>PG</mtext> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mn>8</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> are equal to 45. We also show that there are up to isomorphism three homogeneous pseudo-embeddings of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\textrm{PG}(2,8)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>PG</mtext> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mn>8</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

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The homogeneous pseudo-embeddings of \(\textrm{PG}(2,8)\)

  • Bart De Bruyn,
  • Mou Gao,
  • Dibyayoti Jena

摘要

We show that both the pseudo-embedding and pseudo-generating ranks of the projective plane \(\textrm{PG}(2,8)\) PG ( 2 , 8 ) are equal to 45. We also show that there are up to isomorphism three homogeneous pseudo-embeddings of \(\textrm{PG}(2,8)\) PG ( 2 , 8 ) .