A superadditivity and submultiplicativity property for cardinalities of sumsets

Gyarmati, Katalin and Matolcsi, Máté and Ruzsa, Z. Imre (2010) A superadditivity and submultiplicativity property for cardinalities of sumsets. COMBINATORICA, 30 (2). pp. 163-174. ISSN 0209-9683

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Abstract

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.

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