杂波环境下利用控制确定无平方多项式理想的投射维数
Bounding the Projective Dimension of a Square-Free Monomial Ideal via Domination in Clutters
摘要：
我们在杂波中引入边支配的概念，并使用它来提供任何无平方单项理想的投射维数的上界。然后，我们使用一个简单的递归来恢复一个公式的投射维数的单项式理想相关联的弦杂波，定义由Woodroofe在\cite{russ}。我们还研究了一个家庭的杂波相关的图，并表明，这些杂波弦当且仅当相关的图。最后，我们计算这些杂波的某些类别的支配参数。
英文摘要：
We introduce the concept of edgewise domination in clutters, and use it to provide an upper bound for the projective dimension of any squarefree monomial ideal. We then use a simple recursion to recover a formula for the projective dimension of a monomial ideal associated to a chordal clutter, as defined by Woodroofe in \cite{russ}. We also study a family of clutters associated to graphs, and show that these clutters are chordal if and only if the associated graph is. Finally, we compute domination parameters for certain classes of these clutters.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
