A superadditivity and submultiplicativity property for cardinalities of sumsets

Katalin Gyarmati, Mát́ Matolcsi, Imre Z. Ruzsa

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13 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)163-174
Number of pages12
JournalCombinatorica
Volume30
Issue number2
DOIs
Publication statusPublished - Sep 24 2010

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ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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