What type of study is this?

This is a Experimental Study study.

September 23, 2025Open Access

Additive sumset sizes with tetrahedral differences

Key Points

Popular sumset sizes correspond to differences of tetrahedral numbers in 4-element integer sets.
The research confirms that these sumset sizes are consistently present in the defined sets.
For each identified number, explicit h-adically constructed sets are provided for clarity.
Experimental calculations support the findings, demonstrating the concentration of sumset sizes in specific integer configurations.

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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Cite This Study

Melvyn B. Nathanson (Fri,) studied this question.

synapsesocial.com/papers/68d4764731b076d99fa6df94 https://doi.org/https://doi.org/10.48550/arxiv.2507.08646

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