论文标题
广义递归原子订购和等效到Cl壳性
Generalized recursive atom ordering and equivalence to CL-shellability
论文作者
论文摘要
Björner和Wachs引入了CL壳性，作为研究部分有序集（POSETS）的秩序复合物的拓扑结构的一种技术。他们还提出了递归原子排序的概念，并证明有限的poset在且仅当它承认递归原子订购时都是可CL壳的。 在本文中，引入了递归原子排序概念的概括。事实证明，有限的Poset可以在且仅当它承认传统的递归原子订购时承认这种广义的递归原子订购。事实证明，这也等同于承认具有进一步的属性的属性，称为自偏见。因此，CL壳性被证明等同于自洽的CC壳性。作为一种应用，事实证明，无跨度的posets是平面电网络的分层空间的面部posets，是双重Cl壳。
Björner and Wachs introduced CL-shellability as a technique for studying the topological structure of order complexes of partially ordered sets (posets). They also introduced the notion of recursive atom ordering, and they proved that a finite bounded poset is CL-shellable if and only if it admits a recursive atom ordering. In this paper, a generalization of the notion of recursive atom ordering is introduced. A finite bounded poset is proven to admit such a generalized recursive atom ordering if and only if it admits a traditional recursive atom ordering. This is also proven equivalent to admitting a CC-shelling (a type of shelling introduced by Kozlov) with a further property called self-consistency. Thus, CL-shellability is proven equivalent to self-consistent CC-shellability. As an application, the uncrossing posets, namely the face posets for stratified spaces of planar electrical networks, are proven to be dual CL-shellable.
