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 g 1 …g ℓ 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 ∑ i∈I a i g i = 0 for a i ∈ {+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.