A superadditivity and submultiplicativity property for cardinalities of sumsets

Katalin Gyarmati; Imre Z. Ruzsa; Mate Matolcsi

paper

A superadditivity and submultiplicativity property for cardinalities of sumsets

arXiv:0707.2707

Abstract

For finite sets of integers $A_{1}, A_{2} ... A_{n}$ we study the cardinality of the $n$ -fold sumset $A_{1} + ... + A_{n}$ compared to those of $n - 1$ -fold sumsets $A_{1} + ... + A_{i - 1} + A_{i + 1} + ... A_{n}$ . 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.

9 pages