Tag Archives: Szemeredi’s theorem

Arithmetic progressions and the affine semigroup

— 1. Introduction — Van der Waerden’s theorem on arithmetic progressions states that, given any finite partition of , one of the cells contains arbitrarily long arithmetic progressions. For the sake of completion we give a precise formulation. Theorem 1 … Continue reading

Posted in Combinatorics, Topological Dynamics | Tagged , , | 5 Comments

Brauer’s theorem and a coloring trick of Bergelson

— 1. Introduction — Ramsey theory concerns essentially two types of results: coloring and density results. Coloring results state that given a finite partition of some structured set (usually ) one of the cells in the partition still has some … Continue reading

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