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Periodica Mathematica Hungarica

, Volume 64, Issue 2, pp 213–225 | Cite as

On the Davenport constant and on the structure of extremal zero-sum free sequences

  • Alfred Geroldinger
  • Manfred Liebmann
  • Andreas Philipp
Article

Abstract

Let \(G = C_{n_1 } \oplus \cdots \oplus C_{n_r }\) with 1 < n 1 | … | n r be a finite abelian group, d*(G) = n 1 +…+n r r, and let d(G) denote the maximal length of a zerosum free sequence over G. Then d(G) ≥ d*(G), and the standing conjecture is that equality holds for G = C n r . We show that equality does not hold for C 2C 2n r , where n ≥ 3 is odd and r ≥ 4. This gives new information on the structure of extremal zero-sum free sequences over C 2n r .

Key words and phrases

zero-sum sequence Davenport constant 

Mathematics subject classification numbers

11B30 11P70 20K01 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2012

Authors and Affiliations

  • Alfred Geroldinger
    • 1
  • Manfred Liebmann
    • 1
  • Andreas Philipp
    • 1
  1. 1.Institut für Mathematik und Wissenschaftliches RechnenKarl-Franzens-Universität GrazGrazAustria

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