On sequences over a finite abelian group with zero-sum subsequences of forbidden lengths

Weidong Gao, et al. "On sequences over a finite abelian group with zero-sum subsequences of forbidden lengths." Colloquium Mathematicae 144.1 (2016): 31-44. <http://eudml.org/doc/286582>.

@article{WeidongGao2016,
abstract = {Let G be an additive finite abelian group. For every positive integer ℓ, let $disc_\{ℓ\}(G)$ 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 $disc_\{ℓ\}(G)$ for certain finite groups, including cyclic groups, the groups $G = C₂ ⊕ C_\{2m\}$ 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 $disc(G) = max\{disc_\{ℓ\}(G) | ℓ ≥ 1\}$ and determine disc(G) for finite abelian p-groups G, where p ≥ r(G) and r(G) is the rank of G.},
author = {Weidong Gao, Yuanlin Li, Pingping Zhao, Jujuan Zhuang},
journal = {Colloquium Mathematicae},
keywords = {zero-sum subsequence; Davenport constant; disc(G); disc (G)},
language = {eng},
number = {1},
pages = {31-44},
title = {On sequences over a finite abelian group with zero-sum subsequences of forbidden lengths},
url = {http://eudml.org/doc/286582},
volume = {144},
year = {2016},
}

TY - JOUR
AU - Weidong Gao
AU - Yuanlin Li
AU - Pingping Zhao
AU - Jujuan Zhuang
TI - On sequences over a finite abelian group with zero-sum subsequences of forbidden lengths
JO - Colloquium Mathematicae
PY - 2016
VL - 144
IS - 1
SP - 31
EP - 44
AB - Let G be an additive finite abelian group. For every positive integer ℓ, let $disc_{ℓ}(G)$ 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 $disc_{ℓ}(G)$ for certain finite groups, including cyclic groups, the groups $G = C₂ ⊕ C_{2m}$ 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 $disc(G) = max{disc_{ℓ}(G) | ℓ ≥ 1}$ and determine disc(G) for finite abelian p-groups G, where p ≥ r(G) and r(G) is the rank of G.
LA - eng
KW - zero-sum subsequence; Davenport constant; disc(G); disc (G)
UR - http://eudml.org/doc/286582
ER -