论文标题
一些单一理想的支持poset
Support posets of some monomial ideals
论文作者
论文摘要
单一理想$ i \ subseteq \ mathbf {k} [x_1，\ dots，x_n] $的支持POSET编码变量$ x_1，\ dots，x_n $和$ i $ $ i $的最小单元生成器之间的关系。众所周知，并非每个poset都可以将其视为某些单一理想的支撑位。我们描述了一些posets $ p $，我们可以明确地找到至少一个单一理想$ i_p $，这样$ p $是$ i_p $的支持poset。同样，对于某些单一理想的家庭，我们描述了他们的支持posets并研究其特性。作为应用的一个例子，我们研究了森林与串联理想之间的关系。
The support poset of a monomial ideal $I\subseteq\mathbf{k}[x_1,\dots,x_n]$ encodes the relation between the variables $x_1,\dots,x_n$ and the minimal monomial generators of $I$. It is known that not every poset is realizable as the support poset of some monomial ideal. We describe some posets $P$ for which we can explicitly find at least one monomial ideal $I_P$ such that $P$ is the support poset of $I_P$. Also, for some families of monomial ideals we describe their support posets and study their properties. As an example of application we examine the relation between forests and series-parallel ideals.
