Additive sumset sizes with tetrahedral differences
Number Theory
2025-08-29 v2 Combinatorics
Abstract
Experimental calculations suggest that the -fold sumset sizes of 4-element sets of integers are concentrated at numbers that are differences of tetrahedral numbers. In this paper it is proved that these "popular" sumset sizes always exist. Explicit -adically defined sets are constructed for each of these numbers.
Cite
@article{arxiv.2507.08646,
title = {Additive sumset sizes with tetrahedral differences},
author = {Melvyn B. Nathanson},
journal= {arXiv preprint arXiv:2507.08646},
year = {2025}
}
Comments
Improved exposition; 8 pages