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On the order of elements in long minimal zero-sum sequences

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Abstract

Let G be a finite abelian group and S = \(\prod\nolimits_{i = 1}^l \user1{g} _i \) a minimal zero-sum sequence in G of maximal length |S| = l. We study the order of the elements \(\user1{g}_1 , \ldots ,\user1{g}_\user1{l} \)

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REFERENCES

  1. N. Alon, Combinatorial Nullstellensatz, Combinatorics, Probability and Computing 8 (1999), 7–29.

    Google Scholar 

  2. D. D. Anderson, Factorization in integral domains, Marcel Dekker, 1997.

  3. Y. Caro, Zero-sum problems-A survey, Discrete Math. 152 (1996), 93–113.

    Google Scholar 

  4. S. Chapman, M. Freeze and W. Smith, Minimal zero sequences and the strong Davenport constant, Discrete Math. 203 (1999), 271–277.

    Google Scholar 

  5. S. Chapman and A. Geroldinger, Krull domains and monoids, their sets of lengths and associated combinatorial problems, in: Factorization in integral domains, Lecture Notes in Pure Appl. Math. vol. 189, Marcel Dekker, 1997, 73–112.

  6. W. Gao, On Davenport's constant of finite abelian groups with rank three, Discrete Math. 222 (2000), 111–124.

    Google Scholar 

  7. W. Gao and A. Geroldinger, On long minimal zero sequences in finite abelian groups, Periodica Math. Hungarica 38 (1999), 179–211.

    Google Scholar 

  8. W. Gao and A. Geroldinger, Systems of sets of lengths II, Abhandl. Math. Sem. Univ. Hamburg 70 (2000), 31–49.

    Google Scholar 

  9. A. Geroldinger and R. Schneider, On Davenport's constant, J. Comb. Th. Ser. A 61 (1992), 147–152.

    Google Scholar 

  10. A. Geroldinger and R. Schneider, The cross number of finite abelian groups III, Discrete Math. 150 (1996), 123–130.

    Google Scholar 

  11. J.E. Olson, A combinatorial problem on finite abelian groups I, J. Number Th. 1 (1969), 8–10.

    Google Scholar 

  12. J.E. Olson, A combinatorial problem on finite abelian groups II, J. Number Th. 1 (1969), 195–199.

    Google Scholar 

  13. P. van Emde Boas, A combinatorial problem on finite abelian groups II, in: Reports ZW-1969–007, Math. Centre, Amsterdam, 1969.

    Google Scholar 

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Gao, W., Geroldinger, A. On the order of elements in long minimal zero-sum sequences. Periodica Mathematica Hungarica 44, 63–73 (2002). https://doi.org/10.1023/A:1014923902367

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