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<p>Let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13_2025_2115_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="132" /> </InlineMediaObject> <EquationSource Format="TEX">\(R=K[x_1,\ldots ,x_n]\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mo>=</mo> <mi>K</mi> <mo stretchy="false">[</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation> denote the polynomial ring in <i>n</i> variables over a field <i>K</i> and <i>I</i> be a polymatroidal ideal of <i>R</i>. In this paper, we provide a comprehensive classification of all unmixed polymatroidal ideals. This work addresses a question raised by Herzog and Hibi (Eur J Comb 27:513–517, 2006).</p>

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Unmixed polymatroidal ideals

  • 期刊论文

  • 发表日期：

    2025年3月24日

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  • Mozghan Koolani,
  • Amir Mafi,
  • Hero Saremi

摘要

Let \(R=K[x_1,\ldots ,x_n]\) R = K [ x 1 , … , x n ] denote the polynomial ring in n variables over a field K and I be a polymatroidal ideal of R. In this paper, we provide a comprehensive classification of all unmixed polymatroidal ideals. This work addresses a question raised by Herzog and Hibi (Eur J Comb 27:513–517, 2006).