论文标题
最大链下降订单
Maximal chain descent orders
论文作者
论文摘要
本文在任何有限有限的poset $ p $的最大链上介绍了部分订单，该链条具有Cl标记的$λ$。我们将其称为$λ$引起的最大链下降顺序，表示为$p_λ（2）$。作为一个例子，让$ p $成为布尔晶格，其标准el标记的$λ$给出了$p_λ（2）$同构。有限分布晶格的El标记产生最大的链下降订单，以归因于标准的年轻tableaux的部分订单。我们观察到，人们可能期望的订单关系是覆盖关系，覆盖率是由“多边形移动”所给出的，其传递闭合定义了最大链下降顺序，并不总是覆盖关系。几个例子说明了这一事实。尽管如此，我们表征了每个多边形移动给出覆盖关系的EL标记，我们证明许多众所周知的El标记确实具有预期的覆盖率关系。 $p_λ（2）$的一个动机是，其线性扩展使$ p $的订单复合物的所有炮击都由下降相对于$λ$定义。与$λ$引起的词素图相比，这严格产生的$ p $壳。因此，最大链下降订单$p_λ（2）$可能被认为是编码$λ$引起的炮击的结构。
This paper introduces a partial order on the maximal chains of any finite bounded poset $P$ which has a CL-labeling $λ$. We call this the maximal chain descent order induced by $λ$, denoted $P_λ(2)$. As a first example, letting $P$ be the Boolean lattice and $λ$ its standard EL-labeling gives $P_λ(2)$ isomorphic to the weak order of type A. We discuss in depth other seemingly well-structured examples: the max-min EL-labeling of the partition lattice gives maximal chain descent order isomorphic to a partial order on certain labeled trees, and particular cases of the linear extension EL-labelings of finite distributive lattices produce maximal chain descent orders isomorphic to partial orders on standard Young tableaux. We observe that the order relations which one might expect to be the cover relations, those given by the "polygon moves" whose transitive closure defines the maximal chain descent order, are not always cover relations. Several examples illustrate this fact. Nonetheless, we characterize the EL-labelings for which every polygon move gives a cover relation, and we prove many well known EL-labelings do have the expected cover relations. One motivation for $P_λ(2)$ is that its linear extensions give all of the shellings of the order complex of $P$ whose restriction maps are defined by the descents with respect to $λ$. This yields strictly more shellings of $P$ than the lexicographic ones induced by $λ$. Thus, the maximal chain descent order $P_λ(2)$ might be thought of as encoding the structure of the set of shellings induced by $λ$.
