On Bounds for Two Davenport-type Constants

Let G be an additive abelian group of finite order n and let A be a non-empty set of integers. The Davenport constant of G with weight A, DA(G), is the smallest k ∈ Z+ such that for any sequence x1, . . . , xk of elements in G, there exists a nonempty subsequence xj1 , . . . , xjr and corresponding weights a1, . . . , ar ∈ A such that �r i=1 aixji = 0. Similarly, EA(G) is the smallest positive integer k such that for any sequence x1, . . . , xk of elements in G there exists a non-empty subsequence of exactly n terms, xj1 , . . . , xjn , and corresponding weights a1, . . . , an ∈ A such that �n i=1 aixji = 0. We consider these constants when G = Zn and A = {b2|b ∈ Zn}, proving lower bounds for each.