Additive energies on discrete cubes

Jaume de Dios Pont, Rachel Greenfeld, Paata Ivanisvili +1

We prove that for $d\ge 0$ and $k\ge 2$, for any subset $A$ of a discrete cube $\{0,1{\}}^d$, the $k-$higher energy of $A$ (the number of $2k-$tuples $(a_1,a_2,\dots ,a_{2k})$ in $A…