Vol. 8, No. 1, 2019

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Convex sequences may have thin additive bases

Imre Z. Ruzsa and Dmitrii Zhelezov

Vol. 8 (2019), No. 1, 43–46
DOI: 10.2140/moscow.2019.8.43
Abstract

For a fixed c > 0 we construct an arbitrarily large set B of size n such that its sum set B + B contains a convex sequence of size cn2, answering a question of Hegarty.

Keywords
convex sequences, sumset, additive basis
Mathematical Subject Classification 2010
Primary: 11B13
Milestones
Received: 1 December 2017
Published: 11 August 2018
Authors
Imre Z. Ruzsa
Alfréd Rényi Institute of Mathematics
Hungarian Academy of Sciences
Budapest
Hungary
Dmitrii Zhelezov
Alfréd Rényi Institute of Mathematics
Hungarian Academy of Sciences
Budapest
Hungary