## A triangle theorem for additive energy

#### Brendan MurphyUniversity of RochesterMathematics

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.

Back to Algebraic Techniques for Combinatorial and Computational Geometry