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arXiv · 2409.16233

Addition theorems in partially ordered groups

Melvyn B. Nathanson
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Abstract

Shnirel'man's inequality and Shnirel'man's basis theorem are fundamental results about sums of sets of positive integers in additive number theory. It is proved that these results are inherently order-theoretic and extend to partially ordered abelian and nonabelian groups. One abelian application is an addition theorem for sums of sets of $n$-dimensional lattice points.

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Melvyn B. Nathanson. 2024-09-24. Addition theorems in partially ordered groups. https://arxiv.org/abs/2409.16233

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