Common and Sidorenko Linear Equations
Common and Sidorenko Linear Equations
Abstract A linear equation with coefficients in $\mathbb{F}_q$ is common if the number of monochromatic solutions in any two-coloring of $\mathbb{F}_q^{\,n}$ is asymptotically (as $n \to \infty$) at least the number expected in a random two-coloring. The linear equation is Sidorenko if the number of solutions in any dense subset …