Zero-sum problems — A survey Original Research Article

Zero-sum Ramsey theory is a newly established area in combinatorics. It brings to ramsey theory algebric tools and algebric flavour. The paradigm of zero-sum problems can be formulated as follows: Suppose the elements of a combinatorial structure are mapped into a finite group K. Does there exists a prescribed substructure the sum of the weights of its elements is 0 in K? We survey the algebric background necessary to develop the first steps in this area and its short history dated back to a 1960 theorem of Erdo˝s-Ginzburg and Ziv. Then a systematic survey is made to encompass most of the results published in this area until 1.1.95. Several conjectures and open problems are cited along this manuscript with the hope to catch the eyes of the interested reader