Triangular gaps in the most frequent sizes of $hA$ for $|A|=4$

TL;DR

This paper investigates the occurrence of triangular gaps in the most common sizes of the h-fold sumset for a random four-element subset of natural numbers, revealing patterns through experimental analysis.

Contribution

It provides an explanation for the triangular gaps observed in sumset sizes, based on experimental data for random four-element subsets.

Findings

Triangular gaps are prevalent in the sumset sizes for random 4-element sets.

The gaps are explained through observed patterns in the sumset structure.

Experimental results support the theoretical explanation.

Abstract

We explain the triangular gaps observed experimentally in the most popular sizes of the $h$-fold iterated sumset, $hA,$ when $A$ is a randomly chosen four-element subset of the first $q$ natural numbers, for $q$ much larger than $h.$