Incidence Structures of Type (p, n)

Every incidence structure (understood as a triple of sets (G, M, I), I G×M) admits for every positive integer p an incidence structure where G ^p (M ^p) consists of all independent p-element subsets in G (M) and I ^p is determined by some bijections. In the paper such incidence structures are investigated the 's of which have their incidence graphs of the simple join form. Some concrete illustrations are included with small sets G and M.