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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 ...
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]
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.
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]
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.
Lou Smit, a detective who worked in Colorado Springs law enforcement for decades, came out of retirement at the request of Boulder authorities after the 1996 murder of JonBenet Ramsey (Cindy Marra)
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 .