TY - JOUR
T1 - Zero-sum problems in finite abelian groups and affine caps
AU - Edel, Yves
AU - Elsholtz, Christian
AU - Geroldinger, Alfred
AU - Kubertin, Silke
AU - Rackham, Laurence
PY - 2007/6
Y1 - 2007/6
N2 - For a finite abelian group G, let s(G) denote the smallest integer l such that every sequence S over G of length |S| ≥ l has a zero-sum subsequence of length exp(G). We derive new upper and lower bounds for s(G), and all our bounds are sharp for special types of groups. The results are not restricted to groups G of the form G = Cnr, but they respect the structure of the group. In particular, we show s(Cn4) ≥ 20n - 19 for all odd n, which is sharp if n is a power of 3. Moreover, we investigate the relationship between extremal sequences and maximal caps in finite geometry.
AB - For a finite abelian group G, let s(G) denote the smallest integer l such that every sequence S over G of length |S| ≥ l has a zero-sum subsequence of length exp(G). We derive new upper and lower bounds for s(G), and all our bounds are sharp for special types of groups. The results are not restricted to groups G of the form G = Cnr, but they respect the structure of the group. In particular, we show s(Cn4) ≥ 20n - 19 for all odd n, which is sharp if n is a power of 3. Moreover, we investigate the relationship between extremal sequences and maximal caps in finite geometry.
UR - http://www.scopus.com/inward/record.url?scp=34548427486&partnerID=8YFLogxK
U2 - 10.1093/qmath/ham003
DO - 10.1093/qmath/ham003
M3 - Article
AN - SCOPUS:34548427486
SN - 0033-5606
VL - 58
SP - 159
EP - 186
JO - The Quarterly Journal of Mathematics
JF - The Quarterly Journal of Mathematics
IS - 2
ER -