A Step Beyond Kemperman's Structure Theorem

David J. Grynkiewicz

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arXiv · 0710.1041

A Step Beyond Kemperman's Structure Theorem

David J. Grynkiewicz

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Abstract

A classical result of Kemperman gives a complete recursive description of the structure of those subsets $A$ and $B$ of an abelian group that fail to satisfy the triangle inequality, i.e., $|A+B|<|A|+|B|$. In this paper, we achieve the complete description in the case when equality holds: $|A+B|=|A|+|B|$.

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David J. Grynkiewicz. 2007-10-04. A Step Beyond Kemperman's Structure Theorem. https://arxiv.org/abs/0710.1041

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