Let G be an additive finite abelian group. For every positive integer ℓ, let be the smallest positive integer t such that each sequence S over G of length |S| ≥ t has a nonempty zero-sum subsequence of length not equal to ℓ. In this paper, we determine for certain finite groups, including cyclic groups, the groups and elementary abelian 2-groups. Following Girard, we define disc(G) as the smallest positive integer t such that every sequence S over G with |S| ≥ t has nonempty zero-sum subsequences of distinct lengths. We shall prove that and determine disc(G) for finite abelian p-groups G, where p ≥ r(G) and r(G) is the rank of G.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm6488-8-2015,
author = {Weidong Gao and Yuanlin Li and Pingping Zhao and Jujuan Zhuang},
title = {On sequences over a finite abelian group with zero-sum subsequences of forbidden lengths},
journal = {Colloquium Mathematicae},
volume = {144},
year = {2016},
pages = {31-44},
zbl = {06574989},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6488-8-2015}
}
Weidong Gao; Yuanlin Li; Pingping Zhao; Jujuan Zhuang. On sequences over a finite abelian group with zero-sum subsequences of forbidden lengths. Colloquium Mathematicae, Tome 144 (2016) pp. 31-44. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6488-8-2015/