Linear algebra method

Summary

The linear algebra method bounds the size of a combinatorial family by attaching to each member a vector, or a polynomial, in a vector space. One then proves that these vectors are linearly independent. The size of the family is then at most the dimension of the space. Classic results proved this way include Fisher's inequality and the Oddtown theorem. Its polynomial versions, such as the combinatorial Nullstellensatz and the slice rank argument for the cap set problem, form the polynomial method in combinatorics.