A superadditivity and submultiplicativity property for cardinalities of sumsets

Gyarmati, Katalin; Ruzsa, Imre Z.; Matolcsi, Mate

A superadditivity and submultiplicativity property for cardinalities of sumsets

Authors

Gyarmati, Katalin

Ruzsa, Imre Z.

Matolcsi, Mate

Description

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