Modification of Griffiths' Result for Even Integers

For a finite abelian group G with exp(G) = n, the arithmetical invariant sA(G) is defined to be the least integer k such that any sequence S with length k of elements in G has a A weighted zero-sum subsequence of length n. When A = {1}, it is the Erdős-Ginzburg-Ziv constant and is denoted by s(G). For certain class of sets A, we already have some general bounds for these weighted constants corresponding to the cyclic group Zn, which was given by Griffiths. For odd integer n, Adhikari and Mazumdar generalized the above mentioned results in the sense that they hold for more sets A. In the present paper we modify Griffiths’ method for even n and obtain general bound for the weighted constants for certain class of weighted sets which include sets that were not covered by Griffiths for n ≡ 0 (mod 4).