Schur's Theorem, Van der Waerden's Theorem and the Hales-Jewett Theorem

Jozsef Solymosi
University of British Columbia

The second lecture is an introduction to Ramsey theory. A typical statement sounds something like this; if a large base set with a certain structure partitioned into a few partition classes, then at least one partition class has a subset with a special substructure. For example, Van der Waerden’s theorem states that if the set of natural numbers is partitioned into finitely many classes then one partition class will contain arbitrarily long arithmetic progressions.

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