On additive bases II

Weidong Gao, et al. "On additive bases II." Acta Arithmetica 168.3 (2015): 247-267. <http://eudml.org/doc/278963>.

@article{WeidongGao2015,
abstract = {Let G be an additive finite abelian group, and let S be a sequence over G. We say that S is regular if for every proper subgroup H ⊆ G, S contains at most |H|-1 terms from H. Let ₀(G) be the smallest integer t such that every regular sequence S over G of length |S| ≥ t forms an additive basis of G, i.e., every element of G can be expressed as the sum over a nonempty subsequence of S. The constant ₀(G) has been determined previously only for the elementary abelian groups. In this paper, we determine ₀(G) for some groups including the cyclic groups, the groups of even order, the groups of rank at least five, and all the p-groups except $G=C_p ⊕ C_\{p^n\}$ with n≥ 2.},
author = {Weidong Gao, Dongchun Han, Guoyou Qian, Yongke Qu, Hanbin Zhang},
journal = {Acta Arithmetica},
keywords = {additive basis; regular sequence; 2-zero-sum free set},
language = {eng},
number = {3},
pages = {247-267},
title = {On additive bases II},
url = {http://eudml.org/doc/278963},
volume = {168},
year = {2015},
}

TY - JOUR
AU - Weidong Gao
AU - Dongchun Han
AU - Guoyou Qian
AU - Yongke Qu
AU - Hanbin Zhang
TI - On additive bases II
JO - Acta Arithmetica
PY - 2015
VL - 168
IS - 3
SP - 247
EP - 267
AB - Let G be an additive finite abelian group, and let S be a sequence over G. We say that S is regular if for every proper subgroup H ⊆ G, S contains at most |H|-1 terms from H. Let ₀(G) be the smallest integer t such that every regular sequence S over G of length |S| ≥ t forms an additive basis of G, i.e., every element of G can be expressed as the sum over a nonempty subsequence of S. The constant ₀(G) has been determined previously only for the elementary abelian groups. In this paper, we determine ₀(G) for some groups including the cyclic groups, the groups of even order, the groups of rank at least five, and all the p-groups except $G=C_p ⊕ C_{p^n}$ with n≥ 2.
LA - eng
KW - additive basis; regular sequence; 2-zero-sum free set
UR - http://eudml.org/doc/278963
ER -