Let G be a finite abelian group (written additively), with exponent exp(G) = m and let A be a non-empty subset of {1, 2, . . . , m 1}. The constant A(G) (respectively sA(G)) is defined to be the smallest positive integer t such that any sequence of length t of elements of G contains a non-empty A-weighted zero-sum subsequence of length at most m (respectively, of length equal to m). These generalize the constants (G) and s(G), which correspond to the case A = {1}. In 2007, Gao et al. conjectured that s(G) = (G) + exp(G) 1 for any finite abelian group G; here we shall discuss a similar relation corresponding to the weight A = {1, 1}.
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