Ramsey theory
English[edit]
Etymology[edit]
Named after British mathematician and philosopher Frank P. Ramsey.
Noun[edit]
- (mathematics) A branch of mathematics which deals with patterns that inevitably arise in sufficiently large sets (i.e., subsets of some structure).
- 1987, R. L. Graham, V. Rôdl, Numbers in Ramsey Theory, C. Whitehead (editor), Surveys in Combinatorics 1987: Invited Papers for the Eleventh British Combinatorial Conference, Cambridge University Press, page 111,
- Ramsey theory can be loosely described as the study of structure which is preserved under finite decomposition.
- 1999, Randall McCutcheon, Elemental Methods in Ergodic Ramsey Theory, Springer, Lecture Notes in Mathematics: 1722, page 8,
- We are now ready to offer a loose definition of Ramsey theory.
- Ramsey theory is a collection of results which, given a finite coloring of some structure, guarantee the existence of certain monochromatic configurations or substructures.
- We are now ready to offer a loose definition of Ramsey theory.
- 2015, Ron Graham, Steve Butler, Rudiments of Ramsey Theory, American Mathematical Society, 2nd Edition, page vii,
- In the 35 years since the lectures which form this book were given the area of Ramsey theory has continued to undergo tremendous growth, particularly in the last decade.
- 1987, R. L. Graham, V. Rôdl, Numbers in Ramsey Theory, C. Whitehead (editor), Surveys in Combinatorics 1987: Invited Papers for the Eleventh British Combinatorial Conference, Cambridge University Press, page 111,
Further reading[edit]
- Graham's number on Wikipedia.Wikipedia
- Hales–Jewett theorem on Wikipedia.Wikipedia
- Ramsey's theorem on Wikipedia.Wikipedia
- Van der Waerden's theorem on Wikipedia.Wikipedia