A superadditivity and submultiplicativity property for cardinalities of sumsets

Authors:
Katalin Gyarmati;Máté Matolcsi;Imre Z. Ruzsa
Affiliations:
Alfréd Rényi Institute of Mathematics, Pf. 127, H-1364, Budapest, Hungary;Alfréd Rényi Institute of Mathematics, Pf. 127, H-1364, Budapest, Hungary and BME, Department of Analysis, Egry J. u. 1, H-1111, Budapest, Hungary;Alfréd Rényi Institute of Mathematics, Pf. 127, H-1364, Budapest, Hungary
Venue:
Combinatorica
Year:
2010

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Abstract

For finite sets of integers A 1,…,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.