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<p>The paper is devoted to lower bounds on the independence numbers of distance graphs with vertices in <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11122_2025_5119_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="80" /> </InlineMediaObject> <EquationSource Format="TEX">$\{-1,0,1\}^n$</EquationSource> </InlineEquation>. We study the asymptotic case and obtain new results in a wide range of parameter values. We present numerical results demonstrating nontrivial relationships between the obtained estimates. We separately discuss known upper estimates and their possible nonoptimality.</p>

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Lower Bounds for the Independence Numbers of Distance Graphs with Vertices in \(\{-1,0,1\}^n\)

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • A. R. Akhiiarov,
  • A. V. Bobu,
  • A. M. Raigorodskii

摘要

The paper is devoted to lower bounds on the independence numbers of distance graphs with vertices in $\{-1,0,1\}^n$ . We study the asymptotic case and obtain new results in a wide range of parameter values. We present numerical results demonstrating nontrivial relationships between the obtained estimates. We separately discuss known upper estimates and their possible nonoptimality.