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arXiv · 2601.18507

Robust additive bases without minimal subbases

Daniel Larsen·Michael Larsen
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Abstract

There exists a set $A$ of positive integers such that the number of representations of a large positive integer $m$ as a sum of two elements of $A$ grows with a lower bound of order $\log m$, but for which there is no subset $D$ of $A$ minimal for the property that $D+D$ contains all sufficiently large positive integers.

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Daniel Larsen, Michael Larsen. 2026-01-26. Robust additive bases without minimal subbases. https://arxiv.org/abs/2601.18507

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