Abstract
We want to describe sets that have few sums. If |A|=m, then clearly |A+A|≥m in every group (with equality for cosets), which can be improved to 2m-1 for sets of integers (or torsion-free groups in general). What can we say if we know that |A+A|≤αm, where α is constant or grows slowly as n→∞? That is, we are looking for statements of the form |A|=m, |A+A|≤αm ⇒ (...).
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© 2009 Birkhäuser Verlag
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(2009). Structure of sets with few sums. In: Combinatorial Number Theory and Additive Group Theory. Advanced Courses in Mathematics - CRM Barcelona. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8962-8_11
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DOI: https://doi.org/10.1007/978-3-7643-8962-8_11
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8961-1
Online ISBN: 978-3-7643-8962-8
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