For $(G,+)$ a finite abelian group the plus-minus weighted Davenport constant, denoted $\mathsf{ D}_{ \pm}(G)$, is the smallest $\ell$ such that each sequence $g_1 ... g_{ \ell}$ over $G$ has a weighted zero-subsum with weights +1 and -1, i.e., there is a non-empty subset $I \subset \{ 1,..., \ell\}$ such that $\sum_{ i \in I} a_i g_i =0$ for $a_i \in \{ +1,-1\}$. 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.
Categories: math.NT math.CO