Generalizations of Some Zero-sum Theorems
نویسندگان
چکیده
For a finite abelian group G and a finite subset A ⊆ Z, the Davenport constant of G with weight A, denoted by DA(G), is defined to be the smallest positive integer k such that for any sequence (x1, . . . , xk) of k elements in G there exists a non-empty subsequence (xj1 , . . . , xjr) and a1, . . . , ar ∈ A such that ∑r i=1 ai xji = 0. To avoid trivial cases, one assumes that the weight set A does not contain 0 and it is non-empty. Similarly, for any such A and an abelian group G with |G| = n, the constant EA(G) is the smallest positive integer k such that for any sequence (x1, . . . , xk) of k elements in G there exists xj1 , . . . , xjn such that ∑n i=1 ai xji = 0, with ai ∈ A. In the present paper, we consider the problem of determining EA(n) and DA(n) where A is the set of squares in the group of units in the cyclic group Z/nZ.
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