Tag Archives: combinatorial nullstellensatz

The footprint bound

Studying the set of common zeros of systems of polynomial equations is a fundamental problem in algebra and geometry. In this post we will look at estimating the cardinality of the set of common zeros, when we already know that … Continue reading

Posted in Coding Theory, Combinatorics, Polynomial Method | Tagged , , , , , , , | Leave a comment

Introduction to polynomial method

(The following is a blog-friendly version of Chapter 7 of my PhD thesis, which is an introduction to the so-called polynomial method.) The polynomial method is an umbrella term for different techniques involving polynomials which have been used to solve … Continue reading

Posted in Combinatorics, Incidence Geometry, Polynomial Method | Tagged , , , , | 2 Comments

The coefficient formula and Chevalley-Warning

We discuss the new simultaneous generalization of Chevalley-Warning and Morlaye’s result on polynomial equations over finite fields obtained by Pete Clark. Continue reading

Posted in Number Theory, Polynomial Method | Tagged , , , , , , | 2 Comments