Ramsey theory

Unavoidable monochromatic structure under finite colourings of integers, words, sets and semigroups; graph and ordered-graph Ramsey problems go to GraphTheory, ordinal and infinite-cardinal partition relations to SetTheory, density statements without colouring to additive combinatorics.

• Van der Waerden-type theorems
• Schur and Rado theorems
• Ramsey's theorem, Hales–Jewett and Hindman

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