Category
page 1Ramsey theory
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
Ramsey theory
branch of mathematics
Green–Tao theorem
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
theorem
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
Sim
pencil game