The support poset of a monomial ideal $$I\subseteq {{\mathbf {k}}}[x_1,\ldots ,x_n]$$ encodes the relation between the variables $$x_1,\ldots ,x_n$$ 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.

中文翻译：

---

支持一些单项式理想的偏序集

单项式理想 $$I\subseteq {{\mathbf {k}}}[x_1,\ldots ,x_n]$$ 的支持偏集对变量 $$x_1,\ldots ,x_n$$ 和极小值之间的关系进行编码I 的单项式生成器。众所周知，并不是每个偏序组都可以实现为某个单项式理想的支持偏序组。我们描述了一些偏序集 P，我们可以明确地找到至少一个单项式理想 $$I_P$$ 使得 P 是 $$I_P$$ 的支持偏序集。此外，对于一些单项式理想族，我们描述了它们的支持偏序并研究了它们的性质。作为应用的一个例子，我们研究了森林和串并联理想之间的关系。