zbMATH — the first resource for mathematics

Convex sequences may have thin additive bases. (English) Zbl 1458.11018
The authors prove that there is a \(c>0\) such that for any \(m\) there is a set \(A\) of size \(n>m\) such that the sumset \(A+A\) contains a convex set of size \(cn^2\). This result answers in the affirmative a question posed by P. Hegarty. Here, a set \(A\subset \mathbb{R}\) is convex if the gaps between consecutive elements of \(A\) are strictly increasing.

11B13 Additive bases, including sumsets
Full Text: DOI Euclid
[1] 10.1007/BF01949064 · Zbl 0611.10037
[2] 10.1017/S0963548311000277 · Zbl 1306.11013
[3] 10.1134/S0081543815040185 · Zbl 1383.11014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.