Scholarlink

<p>We introduce the notion of a partial Betti splitting of a homogeneous ideal, generalizing the notion of a Betti splitting first given by Francisco, Hà, and Van Tuyl. Given a homogeneous ideal <i>I</i> and two ideals <i>J</i> and <i>K</i> such that <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(I = J+K\)</EquationSource> </InlineEquation>, a partial Betti splitting of <i>I</i> relates <i>some</i> of the graded Betti numbers of <i>I</i> with those of <i>J</i>,&#xa0;<i>K</i>, and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(J\cap K\)</EquationSource> </InlineEquation>. As an application, we focus on the partial Betti splittings of binomial edge ideals. Using this new technique, we generalize results of Saeedi Madani and Kiani related to binomial edge ideals with cut edges, we describe a partial Betti splitting for all binomial edge ideals, and we compute the total second Betti number of binomial edge ideals of trees.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Partial Betti splittings with applications to binomial edge ideals

  • 期刊论文

  • 发表日期：

    2026年2月11日

查看全文
  • A. V. Jayanthan,
  • Aniketh Sivakumar,
  • Adam Van Tuyl

摘要

We introduce the notion of a partial Betti splitting of a homogeneous ideal, generalizing the notion of a Betti splitting first given by Francisco, Hà, and Van Tuyl. Given a homogeneous ideal I and two ideals J and K such that \(I = J+K\) , a partial Betti splitting of I relates some of the graded Betti numbers of I with those of J, K, and \(J\cap K\) . As an application, we focus on the partial Betti splittings of binomial edge ideals. Using this new technique, we generalize results of Saeedi Madani and Kiani related to binomial edge ideals with cut edges, we describe a partial Betti splitting for all binomial edge ideals, and we compute the total second Betti number of binomial edge ideals of trees.