Monthly Archives: December 2013

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

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Convergence and Recurrence of Z actions

Ergodic Ramsey Theory started with Furstenberg’s proof of Szemeredi’s theorem in arithmetic progressions in 1977. Through a correspondence principle, Furstenberg realized that Szemeredi’s theorem follows from a dynamical statement: for every invertible, ergodic measure preserving transformation of a probability space … Continue reading

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