2022/07/18 by Ren, S.
#05E45 #68P05 #Combinatorics (math.CO) #FOS: Mathematics #Primary 05C80 #Secondary 55U10
paper · doi:10.48550/arxiv.2207.08542
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.