Ramsey theory

English Etymology Named after British mathematician and philosopher Frank P. Ramsey. Noun - en mathematics A branch of mathematics which deals with patterns that inevitably arise in sufficiently large sets (i.e., subsets of some structure). en 1987 R. L. Graham; V. Rôdl Numbers in Ramsey Theory C. Whitehead Surveys in Combinatorics 1987: Invited Papers for the Eleventh British Combinatorial Conference w:Cambridge University Press https://books.google.com.au/books?id=mCA4AAAAIAAJ&pg=PA111&dq=%22Ramsey+theory%22%7C%22Ramsey+theories%22&hl=en&sa=X&ved=0ahUKEwibvvai3bjZAhUMgpAKHekqBCwQ6AEIpQIwMA#v=onepage&q=%22Ramsey%20theory%22%7C%22Ramsey%20theories%22&f=false 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. en 2015 Ron Graham; Steve Butler Rudiments of Ramsey Theory w:American Mathematical Society 2nd https://books.google.com.au/books?id=WpelCgAAQBAJ&pg=PR7&dq=%22Ramsey+theory%22%7C%22Ramsey+theories%22&hl=en&sa=X&ved=0ahUKEwibvvai3bjZAhUMgpAKHekqBCwQ6AEIWDAI#v=onepage&q=%22Ramsey%20theory%22%7C%22Ramsey%20theories%22&f=false 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. Further reading Graham's number Hales–Jewett theorem Ramsey's theorem Van der Waerden's theorem en eponyms