Sumset

Summary

The sumset $A + B$ of two subsets of an abelian group is the set of all sums $a + b$ with $a \in A$ and $b \in B$. It is the basic object of additive combinatorics. Comparing $\abs{A + B}$ with $\abs{A}$ and $\abs{B}$ measures how much additive structure the sets have. For subsets of a vector space the same operation is called Minkowski addition.