Tags » Polynomial Method

The chromatic number of the plane is at least 5

That is:  any coloring of the plane with four colors has two points at distance 1 from each other.  So says a paper just posted by Aubrey de Grey… 207 more words


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… 1,170 more words


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 several problems in finite geometry, discrete geometry, extremal combinatorics and additive number theory. 1,237 more words


The coefficient formula and Chevalley-Warning

This post is about a certain result on coefficients of a multivariate polynomial obtained by Schauz, Lason and Karasev-Petrov, which generalises Alon’s combinatorial nullstellensatz… 665 more words

Polynomial Method

The Erdős-Ginzburg-Ziv Constant (Part II)

Now that we’ve developed a little knowledge about the Combinatorial Nullstellensatz, we can go back and apply it to the problem of computing EGZ constants… 912 more words


The Combinatorial Nullstellensatz

In our last post, we solved a combinatorial problem about 0-sum subsequences by translating it into the language of polynomials. This polynomial method turns out to be a very powerful way to look at problems in combinatorial number theory and other fields. 1,283 more words


The Erdős-Ginzburg-Ziv Constant

Over the course of this summer, I’m taking part in an REU that’s focusing on some problems in additive combinatorics. I thought it would be a good idea to revitalize this blog and put up some notes on my projects throughout the summer, so here we are. 1,113 more words