A superadditivity and submultiplicativity property for cardinalities of sumsets

Details A superadditivity and submultiplicativity property for cardinalities of sumsets A superadditivity and submultiplicativity property for cardinalities of sumsets

2007-07-18

arxiv.org/abs/0707.2707v1

Mathematics

Combinatorics

9 pages

Scientific paper

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.

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