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Of his contributions, the development of Ramsey theory and the application of the probabilistic method especially stand out. Extremal combinatorics owes to him a whole approach, derived in part from the tradition of analytic number theory. Erdős found a proof for Bertrand's postulate which proved to be far neater than Chebyshev's original
Ergodic Ramsey theory is a branch of mathematics where problems motivated by additive combinatorics are proven using ergodic theory. ... Erdős and Turán conjectured ...
In the mathematical theory of infinite graphs, the Erdős–Dushnik–Miller theorem is a form of Ramsey's theorem stating that every infinite graph contains either a countably infinite independent set, or a clique with the same cardinality as the whole graph. [1]
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of the mathematical field of combinatorics that focuses on the appearance of order in a substructure given a structure of a known size. Problems in Ramsey theory typically ask a question of the form: "how big must some structure be to guarantee ...
Erdős on Graphs: His Legacy of Unsolved Problems is a book on unsolved problems in mathematics collected by Paul Erdős in the area of graph theory. It was written by Fan Chung and Ronald Graham, based on a 1997 survey paper by Chung, [1] and published in 1998 by A K Peters. A softcover edition with some updates and corrections followed in 1999.
He did important work in scheduling theory, computational geometry, Ramsey theory, and quasi-randomness, [3] and many topics in mathematics are named after him. He published six books and about 400 papers, and had nearly 200 co-authors, including many collaborative works with his wife Fan Chung and with Paul Erdős.
Rothschild, together with Ronald Graham, formulated one of the most monumental results in Ramsey theory, the Graham–Rothschild theorem. [3] He has collaborated with American mathematicians Joel Spencer and Ronald Graham on key texts related to Ramsey theory. Rothschild wrote several papers with Paul Erdős, giving him an Erdős number of 1. [4]
He has several joint publications with Paul Erdős, and so has Erdős number one. [2] ... He is mostly known for his contributions to Ramsey theory, extremal problems ...