A sumset problem

Javier Cilleruelo, Manuel Almeida Silva, Carlos Vinuesa

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We study the sumset A + k · A for the first non trivial case, k = 3, where k · A = {k · a, a ∈ A}. We prove that |A+ 3 · A| ≥ 4|A|- 4 and that the equality holds only for A = {0, 1, 3}, A = {0, 1, 4}, A = 3 · {0,. . ., n} [ (3 · {0,. . ., n} + 1) and all the affine transforms of these sets.
Original languageEnglish
Title of host publicationA sumset problem
Pages85-96
Number of pages12
Volume2
Edition1
Publication statusPublished - 1 Jan 2012

Publication series

NameJournal of Combinatorics and Number Theory

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  • Cite this

    Cilleruelo, J., Silva, M. A., & Vinuesa, C. (2012). A sumset problem. In A sumset problem (1 ed., Vol. 2, pp. 85-96). (Journal of Combinatorics and Number Theory).