A Step Beyond Kemperman's Structure Theorem

Details A Step Beyond Kemperman's Structure Theorem A Step Beyond Kemperman's Structure Theorem

2007-10-04

arxiv.org/abs/0710.1041v1

Mathematics

Combinatorics

Scientific paper

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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