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Remarks on the plus-minus weighted Davenport constant

Abstract:

For (G, +) a finite abelian group the plus-minus weighted Davenport constant, denoted D±(G), is the smallest ℓ such that each sequence g1...gℓ over G has a weighted zero-subsum with weights +1 and -1, i.e. there is a non-empty subset I ⊂ {1,...,ℓ} such that iI ai gi = 0 for ai {+1, -1}. We present new bounds for this constant, mainly lower bounds, and also obtain the exact value of this constant for various additional types of groups. © World Scientific Publishing Company.