Sumset

In additive combinatorics, the sumset (also called the Minkowski sum) of two subsets

(written additively) is defined to be the set of all sums of an element from

Many of the questions and results of additive combinatorics and additive number theory can be phrased in terms of sumsets.

For example, Lagrange's four-square theorem can be written succinctly in the form where

is the set of square numbers.

A subject that has received a fair amount of study is that of sets with small doubling, where the size of the set