Conjecture on weak sequenceability of abelian groups

Let $t$ be a positive integer, let $G$ be an abelian group, and let $A$ be a finite subset of $G\setminus\{0\}$ with $|A|=k>t$. An ordering of $A$ is a $t$-weak sequencing if its partial sums $s_0,s_1,\ldots,s_k$ satisfy $s_i\ne s_j$ whenever $i\ne j$ and $|i-j|\leq t$; $A$ is $t$-weak sequenceable if it admits such an ordering.

Weak sequenceability conjecture. The set $A$ is $t$-weak sequenceable. Equivalently, every abelian group is $t$-weak sequenceable.

This is a weakening of strong sequenceability motivated by a graph-theoretic interpretation of partial sums as walks with large girth. The paper presents it as an analogue of the Alspach–Liversidge conjecture; no resolution is supplied.