A triangle theorem for additive energy

Brendan Murphy
University of Rochester

Ruzsa's triangle theorem and the Plunnecke-Ruzsa theorem are sumset bounds that control the size of repeated sums of a set in terms of its "doubling constant". Using a variation of Petridis' proof of the Plunnecke-Ruzsa theorem, we prove a lower bound the additive energy of a sumset in terms of the additive energy of its summands.

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