Sums of Dilates in Ordered Groups |
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Authors: | Alain Plagne Salvatore Tringali |
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Institution: | 1. Centre de Mathématiques Laurent Schwartz, école Polytechnique, CNRS, Université Paris–Saclay, Palaiseau Cedex, Franceplagne@math.polytechnique.fr;3. Centre de Mathématiques Laurent Schwartz, école Polytechnique, CNRS, Université Paris–Saclay, Palaiseau Cedex, France |
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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·X + l·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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Keywords: | Additive combinatorics Linearly orderable group Minkowski sumsets Sum of dilates |
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