Zero-sum problems in finite abelian groups and affine caps

Yves Edel*, Christian Elsholtz, Alfred Geroldinger, Silke Kubertin, Laurence Rackham

*Korrespondierende/r Autor/in für diese Arbeit

    Publikation: Beitrag in einer FachzeitschriftArtikel

    Abstract

    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.

    Originalspracheenglisch
    Seiten (von - bis)159-186
    Seitenumfang28
    FachzeitschriftThe Quarterly Journal of Mathematics
    Jahrgang58
    Ausgabenummer2
    DOIs
    PublikationsstatusVeröffentlicht - Jun 2007

    ASJC Scopus subject areas

    • !!Mathematics(all)

    Fingerprint Untersuchen Sie die Forschungsthemen von „Zero-sum problems in finite abelian groups and affine caps“. Zusammen bilden sie einen einzigartigen Fingerprint.

    Dieses zitieren