Intersecting families and nonvanishing multivariate polynomials over finite fields

Shamil Asgarli, Bence Csajbók, Chi Hoi Yip

Let ${\mathcal{P}}_{n,d}$ be the space of polynomials in $n$ variables over ${\mathbb{F}}_q$ of degree at most $d$. Two polynomials $f,g\in {\mathcal{P}}_{n,d}$ intersect if $f(\mathbf a)…