Power monoids: A bridge between factorization theory and arithmetic combinatorics

Power monoids are, in disguise, one of the primary objects of interest in arithmetic combinatorics, and here for the first time we tackle them from the perspective of factorization theory. Proofs lead to consider various properties of finite subsets of N that can or cannot be split into a sumset in a non-trivial way, giving rise to a rich interplay with additive number theory.