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<p>Let <i>J</i> be the cover ideal of a simple graph <i>G</i>. We give a sharp bound for the stability index <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({{\,\textrm{sdstab}\,}}(J)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mspace width="0.166667em" /> <mtext>sdstab</mtext> <mspace width="0.166667em" /> </mrow> <mo stretchy="false">(</mo> <mi>J</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> of the symbolic depth function of <i>J</i>, and this bound is exact if <i>G</i> is a forest.</p>

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Depth stability of cover ideals

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • Mai Phuoc Binh,
  • Nguyen Thu Hang,
  • Truong Thi Hien,
  • Tran Nam Trung

摘要

Let J be the cover ideal of a simple graph G. We give a sharp bound for the stability index \({{\,\textrm{sdstab}\,}}(J)\) sdstab ( J ) of the symbolic depth function of J, and this bound is exact if G is a forest.