论文标题
地图代数的一代随机超图和随机简单复合物
Generations of random hypergraphs and random simplicial complexes by the map algebra
论文作者
论文摘要
我们通过选择每组顶点作为一个随机的超边缘来考虑有限顶点上的随机超图。我们表达了（下）相关的简单复合物和（下）相关的独立性超图的概率分布，从某些随机简单复合物和Erdös-rényi类型的某些随机独立性超图的概率分布表示。我们明确地构建了MAP代数的分级结构，并给出算法以生成随机的超图和随机简单复合物。
We consider the random hypergraph on a finite vertex set by choosing each set of vertices as an hyperedge independently at random. We express the probability distributions of the (lower-)associated simplicial complex and the (lower-)associated independence hypergraph of the random hypergraph in terms of the probability distributions of certain random simplicial complex and certain random independence hypergraph of Erdös-Rényi type. We construct a graded structure of the map algebra explicitly and give algorithms to generate random hypergraphs and random simplicial complexes.
