Abstract
With this chapter, we turn to the second main topic of the course: Subsequence sums and zero-sums. We begin by introducing the modern algebraic language for describing sequences and their subsums, which will be used throughout the remainder of the book. The notion of a setpartition is also introduced along with the basic existence result for n-setpartitions. As a very simple example of the use of setpartitions for finding zero-sums, we give the original proof of the Erdős-Ginzburg-Ziv Theorem, showing that a sequence of 2|G|−1 terms from an abelian group of order |G| must contain a zero-sum subsequence of length |G|. We then introduce the Davenport constant and prove the trivial upper bound: D(G)≤|G|.
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Grynkiewicz, D.J. (2013). Zero-Sums, Setpartitions and Subsequence Sums. In: Structural Additive Theory. Developments in Mathematics, vol 30. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00416-7_10
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DOI: https://doi.org/10.1007/978-3-319-00416-7_10
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