On four colored sets with nondecreasing diameter and the Erdős-Ginzburg-Ziv theorem
A celebrated theorem Erdős-Ginzburg and Ziv asserts that if \(k\), \(m\) are positive integers, \(k|m\), then for every set \(X\) of integers with \(|X|\geq m+k-1\), there exists an \(m\)-element subset \(Y\) of \(X\) for which \(\sum_{y\in Y}y\equiv 0\pmod k\). This theorem is considered as a starting point of zero-sum Ramsey problems. A variety of problems of this topic are investigated. In the present paper the author continues these studies.
scientific article; zbMATH DE number 1888412