Zero-sum problems in finite abelian groups and affine caps

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

    Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

    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

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    Zero-sum Problems
    Finite Abelian Groups
    Finite Geometry
    Zero-sum
    Subsequence
    Upper and Lower Bounds
    Odd
    Denote
    Integer
    Cap

    ASJC Scopus subject areas

    • !!Mathematics(all)

    Dies zitieren

    Zero-sum problems in finite abelian groups and affine caps. / Edel, Yves; Elsholtz, Christian; Geroldinger, Alfred; Kubertin, Silke; Rackham, Laurence.

    in: The quarterly journal of mathematics, Jahrgang 58, Nr. 2, 06.2007, S. 159-186.

    Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

    Edel, Yves ; Elsholtz, Christian ; Geroldinger, Alfred ; Kubertin, Silke ; Rackham, Laurence. / Zero-sum problems in finite abelian groups and affine caps. in: The quarterly journal of mathematics. 2007 ; Jahrgang 58, Nr. 2. S. 159-186.
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    AU - Elsholtz, Christian

    AU - Geroldinger, Alfred

    AU - Kubertin, Silke

    AU - Rackham, Laurence

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