Abstract
The DeVos-Goddyn-Mohar Theorem implies, at least for large n, fairly strong structural conditions on a sequence S when |Σ n (S)| is small. Exercises have explored this is more detail. The aim of this chapter is to extend the potency of such conclusions for finite abelian groups by reducing how large n must be and allowing limited weight sequences as well.
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References
D.J. Grynkiewicz, On a conjecture of Hamidoune for subsequence sums. Integers 5(2), A7 (2005) (electronic)
D.J. Grynkiewicz, On a partition analog of the Cauchy-Davenport theorem. Acta Math. Hung. 107(1–2), 161–174 (2005)
D.J. Grynkiewicz, E. Marchan, O. Ordaz, Representation of finite abelian group elements by subsequence sums. J. Théor. Nr. Bordx. 21(3), 559–587 (2009)
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Grynkiewicz, D.J. (2013). The Partition Theorem II. In: Structural Additive Theory. Developments in Mathematics, vol 30. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00416-7_15
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DOI: https://doi.org/10.1007/978-3-319-00416-7_15
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00415-0
Online ISBN: 978-3-319-00416-7
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