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<p>In this paper, we first show that any square-free monomial ideal in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2922_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="136" /> </InlineMediaObject> <EquationSource Format="TEX">\(K[x_1, x_2, x_3, x_4, x_5]\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo stretchy="false">[</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>4</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>5</mn> </msub> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation> has the strong persistence property. Next, we provide a criterion for a minimal counterexample to the Conforti–Cornuéjols conjecture. Finally, we give a necessary and sufficient condition to determine the normally torsion-freeness of a linear combination of two normally torsion-free square-free monomial ideals.</p>

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On the Strong Persistence Property and Normally Torsion-Freeness of Square-Free Monomial Ideals

  • 期刊论文

  • 发表日期：

    2025年8月8日

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  • Alain Bretto,
  • Mehrdad Nasernejad,
  • Jonathan Toledo

摘要

In this paper, we first show that any square-free monomial ideal in \(K[x_1, x_2, x_3, x_4, x_5]\) K [ x 1 , x 2 , x 3 , x 4 , x 5 ] has the strong persistence property. Next, we provide a criterion for a minimal counterexample to the Conforti–Cornuéjols conjecture. Finally, we give a necessary and sufficient condition to determine the normally torsion-freeness of a linear combination of two normally torsion-free square-free monomial ideals.