论文标题
在细长的矩形晶格上
On slim rectangular lattices
论文作者
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 $ -Sublattice）。我们将$ l $ \ emph {矩形}的$ i = [o，i] $ i = [o，i]），如果有互补的$ a，b \ in i $，以至于$ a $在$ b $的左边。我们声称，细长的矩形晶格的矩形间隔也是一个细长的矩形晶格。我们将介绍一些应用，包括G.Czédli的最新结果。 在大约十几年前的E. knapp的一篇论文中，我们引入了自然图}，用于细长的矩形晶格。五年后，G。Czédli引入了$ {\ e c} _1 $ -Diagrams}我们证明它们是相同的。
Let $L$ be a slim, planar, semimodular lattice (slim means that it does not contain an ${\mathsf M}_3$-sublattice). We call the interval $I = [o, i]$ of $L$ \emph{rectangular}, if there are complementary $a, b \in I$ such that $a$ is to the left of $b$. We claim that a rectangular interval of a slim rectangular lattice is also a slim rectangular lattice. We will present some applications, including a recent result of G. Czédli. In a paper with E. Knapp about a dozen years ago, we introduced natural diagrams} for slim rectangular lattices. Five years later, G. Czédli introduced ${\E C}_1$-diagrams} We prove that they are the same.
