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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 ...
The Erdős–Szekeres conjecture states precisely a more general relationship between the number of points in a general-position point set and its largest subset forming a convex polygon, namely that the smallest number of points for which any general position arrangement contains a convex subset of points is +. It remains unproven, but less ...
Ergodic Ramsey theory is a branch of mathematics where problems motivated by additive combinatorics are proven using ergodic theory. ... Erdős and Turán conjectured ...
In 1930, in a paper entitled 'On a Problem of Formal Logic,' Frank P. Ramsey proved a very general theorem (now known as Ramsey's theorem) of which this theorem is a simple case. This theorem of Ramsey forms the foundation of the area known as Ramsey theory in combinatorics .
Paul Erdős was born on 26 March 1913, in Budapest, Austria-Hungary, [8] the only surviving child of Anna (née Wilhelm) and Lajos Erdős (né Engländer). [9] [10] His two sisters, aged three and five, both died of scarlet fever a few days before he was born. [11]
The Erdős–Heilbronn conjecture in combinatorial number theory on the number of sums of two sets of residues modulo a prime, proved by Dias da Silva and Hamidoune in 1994. [11] The Erdős–Graham conjecture in combinatorial number theory on monochromatic Egyptian fraction representations of unity, proved by Ernie Croot in 2000. [12]
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]
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.