Title: Lagrange-like spectrum of perfect additive complements

Abstract: Two infinite subsets A and B of non-negative integers are called perfect additive complements, if every non-negative integer can be uniquely expressed as the sum of elements from A and B. In this talk, we study the set of possible "sizes" of these sets, that is, we define a Lagrange-like spectrum of the perfect additive complements. As a main result, we show that this set is closed, we obtain the smallest accumulation point, and we show that it contains an interval. We raise also some related open questions. The presented results are joint work with Jin-Hui Fang and Csaba Sándor.