Monthly Archives: March 2014

Pomerance Theorem on colinear points in certain paths in a two dimensional lattice

— 1. Introduction — Van der Waerden’s theorem (to which I gave two proofs in previous posts on this blog) states that if one colors the positive integers with finitely many colors, then one can always find a monochromatic arithmetic … Continue reading

Posted in Combinatorics, Ramsey Theory | Tagged , | 1 Comment

Szemerédi’s Theorem Part III – Precise definitions

This is the third in a series of six posts on Szemerédi’s theorem. In the previous post I outlined the ideas of the ergodic theoretical proof by Furstenberg. In this post I will set up the machinery and give the … Continue reading

Posted in Combinatorics, Ergodic Theory, Ramsey Theory | Tagged , , , | 3 Comments