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arXiv · 1403.0934

Sums of dilates in ordered groups

Alain Plagne·Salvatore Tringali
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Abstract

We address the "sums of dilates problem" by looking for non-trivial lower bounds on sumsets of the form $k \cdot X + l \cdot X$, where $k$ and $l$ are non-zero integers and $X$ is a subset of a possibly non-abelian group $G$ (written additively). In particular, we investigate the extension of some results so far known only for the integers to the context of torsion-free or linearly orderable groups, either abelian or not.

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Alain Plagne, Salvatore Tringali. 2015-02-16. Sums of dilates in ordered groups. https://doi.org/10.1080/00927872.2016.1152476

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