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Inverse zero-sum problems and arithmetical consequences

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Book cover Combinatorial Number Theory and Additive Group Theory

Part of the book series: Advanced Courses in Mathematics - CRM Barcelona ((ACMBIRK))

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Abstract

The investigation of inverse problems has a long tradition in combinatorial number theory (see [107, 37]), and more recently it has been promoted by applications in the theory of non-unique factorizations. In this chapter we discuss the inverse problems associated with the invariants D(G), η(G) and s(G). More precisely, we investigate the structure of sequences of length D(G)−1 (η(G)−1 or s(G)−1, respectively) that do not have a zero-sum subsequence (of the required length). Recent results on the structure of Σ(S) for (long) zero-sum free sequences may be found in [9, 58, 127, 132, 60].

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(2009). Inverse zero-sum problems and arithmetical consequences. In: Combinatorial Number Theory and Additive Group Theory. Advanced Courses in Mathematics - CRM Barcelona. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8962-8_7

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