Binomial coefficients and zero-sum Ramsey numbers
Let \(H\) be a \(k\)-uniform hypergraph and \(G\) be an abelian group. The zero-sum Ramsey number \(R(H,G)\) is the least integer \(n\) such that if the edges of the complete \(k\)-uniform hypergraph \(K_n^k\) are \(G\)-colored, then there is a zero-sum (mod \(G\)) copy of \(H\) in \(K_n^k\). It is shown that the Ramsey number \(R(K_n,Z_p) \leq n + 2p - 2\), and for \(k \geq 2\), \(R(K_n^k,Z_2) \leq n + k\). Precise values of the Ramsey number for some special cases are determined.
scientific article; zbMATH DE number 1093113
scientific article