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<p>We identify several classes of monomial ideals that possess minimal generalized Barile–Macchia resolutions. These classes of ideals include generic monomial ideals, monomial ideals with linear quotients, and edge ideals of hypertrees. We also characterize connected unicyclic graphs whose edge ideals are bridge-friendly and, in particular, have minimal Barile–Macchia resolutions. Barile–Macchia and generalized Barile–Macchia resolutions are cellular resolutions and special types of Morse resolutions.</p>

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Monomial Ideals with Minimal Generalized Barile–Macchia Resolutions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月6日

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  • Trung Chau,
  • Tài Huy Hà,
  • Aryaman Maithani

摘要

We identify several classes of monomial ideals that possess minimal generalized Barile–Macchia resolutions. These classes of ideals include generic monomial ideals, monomial ideals with linear quotients, and edge ideals of hypertrees. We also characterize connected unicyclic graphs whose edge ideals are bridge-friendly and, in particular, have minimal Barile–Macchia resolutions. Barile–Macchia and generalized Barile–Macchia resolutions are cellular resolutions and special types of Morse resolutions.