Some remarks on barycentric-sum problems over cyclic groups

We derive some new results on the k-th barycentric Olson constants of abelian groups (mainly cyclic). This quantity, for a finite abelian (additive) group (G,+), is defined as the smallest integer ℓ such that each subset A of G with at least ℓ elements contains a subset with k elements {g1,…,gk} satisfying g1+⋯+gk=kgj for some 1≤j≤k.