Convex sequences may have thin additive bases

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 $c n^{2}$ , answering a question of Hegarty.

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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

Vol. 8, No. 1, 2019

Imre Z. Ruzsa and Dmitrii Zhelezov

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors