Category

Ramsey theory

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pigeonhole principle

mathematical lemma that, if 𝑛 items are put into 𝑚 containers, with 𝑛>𝑚, then at least one container must contain more than one item

Graham's number

enormously large number, the upper bound solution to a Ramsey theory problem

branch of mathematics

Green–Tao theorem

Ramsey's theorem

combinatorics theorem that any edge labeling of a sufficiently large complete graph contains monochromatic cliques

Happy Ending problem

problem about proving that five points in the plane will have a subset forming the vertices of a convex quadrilateral

Szemerédi's theorem

theorem that long dense subsets of the integers contain arbitrarily large arithmetic progressions

Erdős–Szekeres theorem

theorem that sufficiently long sequences of numbers have long monotonic subsequences

Van der Waerden's theorem

theorem on arithmetic progressions

theorem on friends and strangers

Hales–Jewett theorem

on how much high-dimensional objects must exhibit some combinatorial structure

Boolean Pythagorean triples problem

mathematical problem

zero-sum problem

mathematical problem

Erdős–Burr conjecture

Van der Waerden number

Integer in Ramsey theory