The polynomial method in Galois geometries

Abstract

The polynomial method refers to the application of polynomials to combinatorial problems. The method is particularly effective for Galois geometries and a number of problems and conjectures have been solved using the polynomial method. In many cases the polynomial approach is the only method which we know of that works. In this article, the various polynomial techniques that have been applied to Galois geometries are detailed and, to demonstrate how to apply these techniques, some of the problems referred to above are resolved.

Postprint (published version)