paper

Additive sumset sizes with tetrahedral differences

arXiv:2507.08646

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.

Improved exposition; 8 pages