On common energies and sumsets

TL;DR

This paper introduces a polynomial criterion based on common energy to identify sets with small doubling, advancing the understanding of additive properties in combinatorics.

Contribution

It provides a novel polynomial criterion linking common energy to small doubling in sets, offering a new tool for additive combinatorics.

Findings

Polynomial criterion for small doubling

Connection between common energy and additive structure

Enhanced understanding of sumset properties

Abstract

We obtain a polynomial criterion for a set to have a small doubling in terms of the common energy of its subsets.