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arXiv · 2507.08646

Additive sumset sizes with tetrahedral differences

Melvyn B. Nathanson
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Abstract

Experimental calculations suggest that the $h$-fold sumset sizes of 4-element sets of integers are concentrated at $h$ numbers that are differences of tetrahedral numbers. In this paper it is proved that these "popular" sumset sizes always exist. Explicit $h$-adically defined sets are constructed for each of these numbers.

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Melvyn B. Nathanson. 2025-07-11. Additive sumset sizes with tetrahedral differences. https://arxiv.org/abs/2507.08646

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