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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]
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 ...
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.
The Integrated Psychological Theory of leadership attempts to integrate the strengths of the older theories (i.e. traits, behavioral/styles, situational and functional) while addressing their limitations, introducing a new element – the need for leaders to develop their leadership presence, attitude toward others, and behavioral flexibility ...
Ramsey's theorem states that such a number exists for all m and n. By symmetry, it is true that R(m, n) = R(n, m). An upper bound for R(r, s) can be extracted from the proof of the theorem, and other arguments give lower bounds. (The first exponential lower bound was obtained by Paul Erdős using the probabilistic method.) However, there is a ...
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 .
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.