论文标题
半模化晶格中的两个标志会产生抗膜质
Two flags in a semimodular lattice generate an antimatroid
论文作者
论文摘要
模块化晶格中的基本属性是，任何两个标志都会生成分布式sublattice。据显示（Abels 1991，Herscovic 1998），半模型晶格中的两个旗帜不再产生如此良好的sublattice，而将它们连接起来的最短画廊形成了相对较好的联盟宣传。在本说明中，我们对这项研究进行了加强，以建立半模化晶格的两型型生成定理的类似物。我们考虑一个模块化凸子集的概念，该子集是在联接下关闭的子集，仅与模块化对相遇，并表明，在等级$ n $的半模块化晶格中，两个标志的模块化凸壳对$ n $的$ n $ n $ n $ n $是同构。这个家庭独特地确定了一种抗膜质，这与两个旗帜的最短画廊的联接共同伴侣。
A basic property in a modular lattice is that any two flags generate a distributive sublattice. It is shown (Abels 1991, Herscovic 1998) that two flags in a semimodular lattice no longer generate such a good sublattice, whereas shortest galleries connecting them form a relatively good join-sublattice. In this note, we sharpen this investigation to establish an analogue of the two-flag generation theorem for a semimodular lattice. We consider the notion of a modular convex subset, which is a subset closed under the join and meet only for modular pairs, and show that the modular convex hull of two flags in a semimodular lattice of rank $n$ is isomorphic to a union-closed family on $[n]$. This family uniquely determines an antimatroid, which coincides with the join-sublattice of shortest galleries of the two flags.
