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<p>We study further monomial ideals with regular quotients, which can be seen as an extension of monomial ideals with linear quotients. Based on these investigations, we are able to calculate the Betti numbers of toric ideals belonging to various classes of edge rings. One of main results from Bhaskara and Van Tuyl (Proc. Amer. Math. Soc. Ser. B. <b>10</b>, 219–232, <CitationRef CitationID="CR2">2023</CitationRef>) is recovered.</p>

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Monomial Ideals with Regular Quotients and Some Families of Edge Rings

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Dancheng Lu,
  • Hao Zhou

摘要

We study further monomial ideals with regular quotients, which can be seen as an extension of monomial ideals with linear quotients. Based on these investigations, we are able to calculate the Betti numbers of toric ideals belonging to various classes of edge rings. One of main results from Bhaskara and Van Tuyl (Proc. Amer. Math. Soc. Ser. B. 10, 219–232, 2023) is recovered.