For finite sets of integers A1,...,An we study the cardinality of the n-fold sumset A1+...+ An compared to those of (n-1)-fold sumsets A1+...+Ai-1+Ai+1+...+An. We prove a superadditivity and a submultiplicativity property for these quantities. We also examine the case when the addition of elements is restricted to an addition graph between the sets.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Computational Mathematics