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The structure of maximal zerosum free sequences
"... This paper is a continuation of our investigation of zerosum (free) sequences of finite abelian groups (see [3] or [4]). As is the tradition, we let G be a finite abelian group, A ⊆ G a multiset and we say that A is zerosum free if there exists no nonempty subset B ⊆ A, such that ∑ ..."
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This paper is a continuation of our investigation of zerosum (free) sequences of finite abelian groups (see [3] or [4]). As is the tradition, we let G be a finite abelian group, A ⊆ G a multiset and we say that A is zerosum free if there exists no nonempty subset B ⊆ A, such that ∑
Inductive Methods and zerosum free sequences, Integers
"... Abstract. A fairly long standing conjecture was that the Davenport constant of a group G = Zn1 ⊕ · · · ⊕ Zn k with n1 ... nk is 1 + Pk i=1 (ni − 1). This conjecture is false in general, but the question remains for which groups it is true. By using inductive methods we prove that for two fixed ..."
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Abstract. A fairly long standing conjecture was that the Davenport constant of a group G = Zn1 ⊕ · · · ⊕ Zn k with n1 ... nk is 1 + Pk i=1 (ni − 1). This conjecture is false in general, but the question remains for which groups it is true. By using inductive methods we prove that for two fixed integers k and ℓ it is possible to decide whether the conjecture is satisfied for all groups of the form Zℓ k ⊕ Zn with n coprime to k. We also prove the conjecture for groups of the form Z3 ⊕ Z3n ⊕ Z3n, where n is coprime to 6, assuming a conjecture about the maximal zerosum free sets in Z2 n.
DOI 10.1515/INTEG.2009.0xy © de Gruyter 2009 Inductive Methods and ZeroSum Free Sequences
"... Abstract. A fairly longstanding conjecture is that the Davenport constant of a group G D Zn1 ˚ ˚ Znk with n1 j j nk is 1C Pk iD1.ni 1/. This conjecture is false in general, but it remains to know for which groups it is true. By using inductive methods we prove that for two fixed intege ..."
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Abstract. A fairly longstanding conjecture is that the Davenport constant of a group G D Zn1 ˚ ˚ Znk with n1 j j nk is 1C Pk iD1.ni 1/. This conjecture is false in general, but it remains to know for which groups it is true. By using inductive methods we prove that for two fixed integers k and ` it is possible to decide whether the conjecture is satisfied for all groups of the form Z` k ˚ Zn with n coprime to k. We also prove the conjecture for groups of the form Z3˚Z3n˚Z3n; where n is coprime to 6, assuming a conjecture about the maximal zerosum free sets in Z2n.