论文标题
另一项研究说明
Another research note
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论文摘要
令$ l $为苗条，平面，半模块晶格（Slim表示它不包含$ {\ Mathsf M} _3 $ -Sublattices）。 We call the interval $I = [o, i]$ of $L$ \emph{rectangular}, if there are $u_l, u_r \in [o, i] - \{o,i\}$ such that $i = u_l \vee u_r$ and $o = u_l \wedge u_r$ where $u_l$ is to the left of $u_r$. \ emph {第一个结果}：矩形晶格的矩形间隔是矩形晶格。作为应用程序，我们获得了G.Czédli的最新结果。 在2017年的论文中，G。czédli引入了一个非常强大的图表类型，用于纤毛，平面，半模块化晶格，\ emph {$ \ Mathcal {c} _1 $ -diagrams}。 我们重新审视了\ emph {自然图}的概念。考虑到一个细长的矩形晶格$ L $，我们在一个简单的步骤中构建了自然图。 \ emph {第二个结果}表明，对于纤细的矩形晶格，一个自然图与$ \ Mathcal {C} _1 $ -Diagram相同。因此，自然图具有$ \ Mathcal {C} _1 $ -Diagrams的所有不错的属性。
Let $L$ be a slim, planar, semimodular lattice (slim means that it does not contain ${\mathsf M}_3$-sublattices). We call the interval $I = [o, i]$ of $L$ \emph{rectangular}, if there are $u_l, u_r \in [o, i] - \{o,i\}$ such that $i = u_l \vee u_r$ and $o = u_l \wedge u_r$ where $u_l$ is to the left of $u_r$. \emph{The first result}: a rectangular interval of a rectangular lattice is a rectangular lattice. As an application, we get a recent result of G. Czédli. In a 2017 paper, G. Czédli introduced a very powerful diagram type for slim, planar, semimodular lattices, the \emph{$\mathcal{C}_1$-diagrams}. We revisit the concept of \emph{natural diagrams} I introduced with E.~Knapp about a dozen years ago. Given a slim rectangular lattice $L$, we construct its natural diagram in one simple step. \emph{The second result} shows that for a slim rectangular lattice, a~natural diagram is the same as a $\mathcal{C}_1$-diagram. Therefore, natural diagrams have all the nice properties of $\mathcal{C}_1$-diagrams.
