论文标题
在双cpt和强-cpt posets上
On dually-CPT and strong-CPT posets
论文作者
论文摘要
POSET是树（CPT）中的路径的遏制，如果poset的每个元素由树中的每个元素表示，而当poset中的每个元素都可以在Poset中表示，则仅当相应的路径与包含关系相关时。最近，Alcón，Gudiño和Gutierrez引入了CPT POSET的适当子类，即DLAILE-CPT和强烈cpt。 poset $ \ mathbf {p} $是双重cpt，并且仅当$ \ mathbf {p} $及其dual $ \ mathbf {p}^{d} $都允许cpt表示。 poset $ \ mathbf {p} $在且仅当$ \ mathbf {p} $以及共享相同基础可比性图的所有posets时才强烈cpt。众所周知，由于双重CPT和CPT之间的包含是严格的。 Alcón，Gudiño和Gutierrez将其作为一个悬而未决的问题提出，是否强烈cpt是双重cpt的严格子类。我们提供了两个课程实际上一致的证明。
A poset is a containment of paths in a tree (CPT) if it admits a representation by containment where each element of the poset is represented by a path in a tree and two elements are comparable in the poset if and only if the corresponding paths are related by the inclusion relation. Recently Alcón, Gudiño and Gutierrez introduced proper subclasses of CPT posets, namely dually-CPT, and strongly-CPT. A poset $\mathbf{P}$ is dually-CPT, if and only if $\mathbf{P}$ and its dual $\mathbf{P}^{d}$ both admit a CPT representation. A poset $\mathbf{P}$ is strongly-CPT, if and only if $\mathbf{P}$ and all the posets that share the same underlying comparability graph admit a CPT representation. Where as the inclusion between Dually-CPT and CPT was known to be strict. It was raised as an open question by Alcón, Gudiño and Gutierrez whether strongly-CPT was a strict subclass of dually-CPT. We provide a proof that both classes actually coincide.
