Let A = {a1, . . . , ak} and B = {b1, . . . , bk} be two subsets of an Abelian group G, k ≤ |G|. Snevily conjectured that, when G is of odd order, there is a permutation π ∈ Sk such that the sums… (More)

In this expository paper we collect some combinatorial problems in the additive theory that can be easily solved in ordered Abelian groups. We study how such results, obtained by simple combinatorial… (More)

Let S be a point set in the plane in general position, such that its elements are partitioned into k classes or colors. In this paper we study several variants on problems related to the… (More)

Eszter Klein’s theorem claims that among any 5 points in the plane, no three collinear, there is the vertex set of a convex quadrilateral. An application of Ramsey’s theorem then yields the classical… (More)

Let A and B be nonempty subsets of a finite group G in which the order of the smallest nonzero subgroup is not smaller than d = |A| + |B| − 1. Then at least d different elements of G has a… (More)

Let C n denote the cycle of length n. The generalized Ramsey number of the pair (C n ; C k), denoted by R(C n ; C k), is the smallest positive integer R such that any complete graph with R vertices… (More)

Let A be a set of k elements of an Abelian group G in which the order of the smallest nonzero subgroup is at least 2k − 3. Then the number of different elements of G that can be written in the form a… (More)