Dion Gijswijt

Excluding affine configurations over a finite field

2021 · arXiv (Cornell University)

Let $a_{i1}x_1+\cdots+a_{ik}x_k=0$, $i\in[m]$ be a balanced homogeneous system of linear equations with coefficients $a_{ij}$ from a finite field $\mathbb{F}_q$. We say that a solution $x=(x_1,\ldots, x_k)$ with $x_1,\ldots, x_k\in \mathbb{F}_q^n$ is `generic' if every homogeneous …