{c}

Let $p$ be a <prime number>, let $L\subseteq\mathbb F_p$ have $s\leq\min\{k,n-k\}$ elements, and suppose $\mathcal A\subseteq[n]^{(k)}$ satisfies $|A\cap B|\bmod p\in L$ for distinct members while $k\bmod p\notin L$. The Frankl-Wilson theorem gives
$$
|\mathcal A|\leq\binom ns.
$$
Its <polynomial method in combinatorics> turns modular intersection restrictions into linearly independent functions represented by square-free monomials of degree $s$.


Frankl-Wilson theorem

{wiki=Polynomial_method_in_combinatorics}

The polynomial method in combinatorics encodes a discrete configuration by polynomials and obtains combinatorial bounds from their degree, zeros, coefficients, or linear independence.


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