= Nonuniform Frankl-Wilson theorem
{title2=$|\mathcal F|\leq\sum_{j=0}^s\binom nj$}
Let $p$ be a <prime number> and $L\subseteq\mathbb F_p$ have $s$ elements. A <set family> whose member sizes modulo $p$ avoid $L$, and whose distinct pairwise intersection sizes modulo $p$ belong to $L$, has at most $\sum_{j=0}^{\min(s,n)}\binom nj$ members. The <intersection polynomials> $\prod_{\ell\in L}(\sum_{i\in A}x_i-\ell)$ have a diagonal, nonzero evaluation matrix on the family's <characteristic vectors of sets>. <Multilinear reduction on the Boolean cube> places these <linearly independent> functions in the space spanned by square-free <monomials> of degree at most $s$.
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