论文标题
充足的简单络合物
Ample simplicial complexes
论文作者
论文摘要
由网络理论，工程和计算机科学中潜在应用的动机，我们研究$ r $ $ - 样品简单复合物。这些络合物可以看作是对Rado复合物的有限近似值，它具有{\ IT坚不可摧，}的显着特性，因为它去除了任何有限数量的单纯糖，使其本身具有复杂的同构。我们证明，$ r $ - 样品简单综合体是简单的连接，$ 2 $连接，以$ r $ $大。 $ r $ - 样品简单复合物的顶点的数字$ n $满足$ \ exp（ω（\ frac {2^r} {\ sqrt {r}}}））$。我们使用概率方法来确定任何$ n $ dertexes的$ r $ pample simplicial复合物，用于任何$ n> r 2^r 2^{2^r} $。最后，我们介绍了迭代的Paley Simplicial Complextes，它们是明确构造的$ r $ r $ pample简单络合物，具有几乎最佳的顶点。
Motivated by potential applications in network theory, engineering and computer science, we study $r$-ample simplicial complexes. These complexes can be viewed as finite approximations to the Rado complex which has a remarkable property of {\it indestructibility,} in the sense that removing any finite number of its simplexes leaves a complex isomorphic to itself. We prove that an $r$-ample simplicial complex is simply connected and $2$-connected for $r$ large. The number $n$ of vertexes of an $r$-ample simplicial complex satisfies $\exp(Ω(\frac{2^r}{\sqrt{r}}))$. We use the probabilistic method to establish the existence of $r$-ample simplicial complexes with $n$ vertexes for any $n>r 2^r 2^{2^r}$. Finally, we introduce the iterated Paley simplicial complexes, which are explicitly constructed $r$-ample simplicial complexes with nearly optimal number of vertexes.
