Binomial Coefficients and Zero-Sum Ramsey Numbers

A counting argument is developed and divisibility properties of the binomial coefficients are combined to prove, among other results, that[formula]whereKn, resp.Kkn, is the complete, resp. completek-uniform, hypergaph andR(Kn, Zp),R(Kkn, Z2) are the corresponding zero-sum Ramsey numbers.