On a different weighted zero-sum constant

Abstract

For a finite abelian group (G,+), the constant C(G) is defined to be the smallest natural number k such that any sequence in G having length k will have a subsequence of consecutive terms whose sum is zero. For a subset A of Zn, the constant CA(n) is the smallest natural number k such that any sequence in G having length k will have an A-weighted zero-sum subsequence of consecutive terms. We determine the value of CA(n) for some weight-sets A which are related to units in Zn.