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ON SUBSEQUENCE SUMS OF ZERO-SUM FREE SEQUENCES OVER $C_8 \oplus C_8$
Keywords:
abelian group, subsequence sums, zero-sum freeDOI:
https://doi.org/10.17654/0972555522020Abstract
Let $G$ be a finite abelian group and $S$ be a sequence with terms in $G$. Let $\Sigma(S) \subset G$ denote the set of group elements which can be expressed as a sum of terms of a nonempty subsequence of $S$. We call $S$ zero-sum free if $0 \notin \Sigma(S)$. In this paper, we determine the lower bound of $|\Sigma(S)|$ when $S$ is a zero-sum free sequence of elements from $G=C_8 \oplus C_8$ with $8 \leq|S| \leq 14$. This gives a positive answer to a case of a conjecture of Bollobás and Leader.
Received: May 6, 2022
Accepted: May 14, 2022
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