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<p>We present a proof of the extension property for partial automorphisms (EPPA) for classes of finite <i>n</i>-partite tournaments for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="493_2025_179_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="125" /> </InlineMediaObject> <EquationSource Format="TEX">\(n \in \{2,3,\ldots ,\omega \}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>∈</mo> <mo stretchy="false">{</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>, and for the class of finite semigeneric tournaments. We also prove that the generic <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="493_2025_179_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation>-partite tournament and the generic semigeneric tournament have ample generics.</p>

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Extension Property for Partial Automorphisms of the n-partite and Semigeneric Tournaments

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月26日

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  • Jan Hubička,
  • Colin Jahel,
  • Matěj Konečný,
  • Marcin Sabok

摘要

We present a proof of the extension property for partial automorphisms (EPPA) for classes of finite n-partite tournaments for \(n \in \{2,3,\ldots ,\omega \}\) n ∈ { 2 , 3 , … , ω } , and for the class of finite semigeneric tournaments. We also prove that the generic \(\omega \) ω -partite tournament and the generic semigeneric tournament have ample generics.