Let $G$ be a finite abelian group. It is well known that every sequence $S$ over $G$ of length at least $|G|$ contains a zero-sum subsequence of length at most $\mathsf{h}(S)$, where $\mathsf{h}(S)$ is the maximal multiplicity of elements occurring in $S$. It is interesting to study the corresponding inverse problem, that is to find information on the structure of the sequence $S$ which does not contain zero-sum subsequences of length at most $\mathsf{h}(S)$. Under the assumption that $|\sum(S)|< \min\{|G|,2|S|-1\}$, Gao, Peng and Wang showed that such a sequence $S$ must be strictly behaving. In the present paper, we explicitly give the structure of such a sequence $S$ under the assumption that $|\sum(S)|=2|S|-1<|G|$.
@article{10_37236_11963,
author = {Xiangneng Zeng and Pingzhi Yuan},
title = {On sequences without short zero-sum subsequences},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {4},
doi = {10.37236/11963},
zbl = {1536.11050},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11963/}
}
TY - JOUR
AU - Xiangneng Zeng
AU - Pingzhi Yuan
TI - On sequences without short zero-sum subsequences
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/11963/
DO - 10.37236/11963
ID - 10_37236_11963
ER -
%0 Journal Article
%A Xiangneng Zeng
%A Pingzhi Yuan
%T On sequences without short zero-sum subsequences
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/11963/
%R 10.37236/11963
%F 10_37236_11963
Xiangneng Zeng; Pingzhi Yuan. On sequences without short zero-sum subsequences. The electronic journal of combinatorics, Tome 30 (2023) no. 4. doi: 10.37236/11963
