LOWER BOUNDS OF RAMSEY NUMBERS

The lower bounds for any R(l,…,l;r)are investigated.Let K~r be the completer-uniform hypergraph on n points.Define R(l,…,l;r)as the minimal natural number n sothat if the edges of K~r are q-colored,there is a set S of l(i∈{1,…,q})vertices such that alledges on S are of the i-th color.For the special case of q=r=2,the lower bounds were got byP.Erd(?)s and J.Spencer.In this paper,we shall give the lower bounds for any R(l,…,l;r).