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Lajos Pósa (mathematician)
Lajos Pósa (born 9 December 1947 in Budapest) is a Hungarian mathematician working in the topic of combinatorics, and one of the most prominent mathematics educators of Hungary, best known for his mathematics camps for gifted students. He is a winner of the Széchenyi Prize. Paul Erdős's favorite "child", he discovered theorems at the age of 13. Since 2002, he has worked at the Rényi Institute of the Hungarian Academy of Sciences; earlier he was at the Eötvös Loránd University, at the Departments of Mathematical Analysis, Computer Science. Biography He was born in Budapest, Hungary on 9 December 1947. His father was a chemist, his mother a mathematics teacher. He was a child prodigy. While still in elementary school, the educator Rózsa Péter, friend of his mother introduced him to Paul Erdős, who invited him for lunch in a restaurant, and bombarded him with mathematical questions. Pósa finished the problems sooner than his soup, which impressed Erdős, who himself ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Budapest
Budapest is the Capital city, capital and List of cities and towns of Hungary, most populous city of Hungary. It is the List of cities in the European Union by population within city limits, tenth-largest city in the European Union by population within city limits and the List of cities and towns on the river Danube, second-largest city on the river Danube. The estimated population of the city in 2025 is 1,782,240. This includes the city's population and surrounding suburban areas, over a land area of about . Budapest, which is both a List of cities and towns of Hungary, city and Counties of Hungary, municipality, forms the centre of the Budapest metropolitan area, which has an area of and a population of 3,019,479. It is a primate city, constituting 33% of the population of Hungary. The history of Budapest began when an early Celts, Celtic settlement transformed into the Ancient Rome, Roman town of Aquincum, the capital of Pannonia Inferior, Lower Pannonia. The Hungarian p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulgaria
Bulgaria, officially the Republic of Bulgaria, is a country in Southeast Europe. It is situated on the eastern portion of the Balkans directly south of the Danube river and west of the Black Sea. Bulgaria is bordered by Greece and Turkey to the south, Serbia and North Macedonia to the west, and Romania to the north. It covers a territory of and is the tenth largest within the European Union and the List of European countries by area, sixteenth-largest country in Europe by area. Sofia is the nation's capital and List of cities and towns in Bulgaria, largest city; other major cities include Burgas, Plovdiv, and Varna, Bulgaria, Varna. One of the earliest societies in the lands of modern-day Bulgaria was the Karanovo culture (6,500 BC). In the 6th to 3rd century BC, the region was a battleground for ancient Thracians, Persians, Celts and Ancient Macedonians, Macedonians; stability came when the Roman Empire conquered the region in AD 45. After the Roman state splintered, trib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Pósa Theorem
In the mathematical discipline of graph theory, the Erdős–Pósa theorem, named after Paul Erdős and Lajos Pósa, relates two parameters of a graph: * The size of the largest collection of vertex-disjoint cycles contained in the graph; * The size of the smallest feedback vertex set in the graph: a set that contains one vertex from every cycle. Motivation and statement In many applications, we are interested in finding a minimum feedback vertex set in a graph: a small set that includes one vertex from every cycle, or, equivalently, a small set of vertices whose removal destroys all cycles. This is a hard computational problem; if we are not able to solve it exactly, we can instead try to find lower and upper bounds on the size of the minimum feedback vertex set. One approach to find lower bounds is to find a collection of vertex-disjoint cycles in a graph. For example, consider the graph in Figure 1. The cycles A-B-C-F-A and G-H-I-J-G share no vertices. As a result, if we wan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Endre Szemerédi
Endre Szemerédi (; born August 21, 1940) is a Hungarian-American mathematician and computer scientist, working in the field of combinatorics and theoretical computer science. He has been the State of New Jersey Professor of computer science at Rutgers University since 1986. He also holds a professor emeritus status at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences. Szemerédi has won prizes in mathematics and science, including the Abel Prize in 2012. He has made a number of discoveries in combinatorics and computer science, including Szemerédi's theorem, the Szemerédi regularity lemma, the Erdős–Szemerédi theorem, the Hajnal–Szemerédi theorem and the Szemerédi–Trotter theorem. Early life Szemerédi was born in Budapest. Since his parents wished him to become a doctor, Szemerédi enrolled at a college of medicine, but he dropped out after six months (in an interview he explained it: "I was not sure I could do work bearing su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
János Komlós (mathematician)
János Komlós (born 23 May 1942, in Budapest) is a Hungarian-American mathematician, working in probability theory and discrete mathematics. He has been a professor of mathematics at Rutgers University since 1988. He graduated from the Eötvös Loránd University, then became a fellow at the Mathematical Institute of the Hungarian Academy of Sciences. Between 1984–1988 he worked at the University of California, San Diego. Notable results * Komlós' theorem: He proved that every L1-bounded sequence of real functions contains a subsequence such that the arithmetic means of all its subsequences converge pointwise almost everywhere. In probabilistic terminology, the theorem is as follows. Let ξ1,ξ2,... be a sequence of random variables such that ''E'' �1''E'' �2... is bounded. Then there exist a subsequence ξ'1, ξ'2,... and a random variable β such that for each further subsequence η1,η2,... of ξ'0, ξ'1,... we have (η1+...+ηn)/n → β a.s. * With Miklós Ajtai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfréd Rényi
Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician known for his work in probability theory, though he also made contributions in combinatorics, graph theory, and number theory. Life Rényi was born in Budapest to Artúr Rényi and Borbála Alexander; his father was a mechanical engineer, while his mother was the daughter of philosopher and literary critic Bernhard Alexander; his uncle was Franz Alexander, a Hungarian-American psychoanalyst and physician. He was prevented from enrolling in university in 1939 due to the anti-Jewish laws then in force, but enrolled at the University of Budapest in 1940 and finished his studies in 1944. At this point, he was drafted to forced labour service, from which he managed to escape during transportation of his company. He was in hiding with false documents for six months. Biographers tell an incredible story about Rényi: after half of a year in hiding, he managed to get hold of a soldier's uniform and march ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Graph
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective, random graphs are used to answer questions about the properties of ''typical'' graphs. Its practical applications are found in all areas in which complex networks need to be modeled – many random graph models are thus known, mirroring the diverse types of complex networks encountered in different areas. In a mathematical context, ''random graph'' refers almost exclusively to the Erdős–Rényi random graph model. In other contexts, any graph model may be referred to as a ''random graph''. Models A random graph is obtained by starting with a set of ''n'' isolated vertices and adding successive edges between them at random. The a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian Path
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once. A Hamiltonian path that starts and ends at adjacent vertices can be completed by adding one more edge to form a Hamiltonian cycle, and removing any edge from a Hamiltonian cycle produces a Hamiltonian path. The computational problems of determining whether such paths and cycles exist in graphs are NP-complete; see Hamiltonian path problem for details. Hamiltonian paths and cycles are named after William Rowan Hamilton, who invented the icosian game, now also known as ''Hamilton's puzzle'', which involves finding a Hamiltonian cycle in the edge graph of the dodecahedron. Hamilton solved this problem using the icosian calculus, an algebraic structure based on roots of unity with many similarities to the quaternions (also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imre Z
Imre () is a Hungarian masculine first name, which is also in Estonian use, where the corresponding name day is 10 April. It has been suggested that it relates to the name Emeric, Emmerich or Heinrich. Its English equivalents are Emery and Henry. Bearers of the name include the following (who generally held Hungarian nationality, unless otherwise noted): * Imre Antal (1935–2008), pianist * Imre Bajor (1957–2014), actor * Imre Bebek (d. 1395), baron * Imre Bródy (1891–1944), physicist * Imre Bujdosó (b. 1959), Olympic fencer * Imre Csáky (cardinal) (1672–1732), Roman Catholic cardinal * Imre Csermelyi (b. 1988), football player *Imre Cseszneky (1804–1874), agriculturist and patriot * Imre Csiszár (b. 1938), mathematician * Imre Csösz (b. 1969), Olympic judoka * Imre Czobor (1520–1581), Noble and statesman *Imre Czomba (b. 1972), Composer and musician * Imre Deme (b. 1983), football player * Imre Erdődy (1889–1973), Olympic gymnast * Imre Farkas (1879–1976 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Péter Komjáth
Péter Komjáth (born 8 April 1953) is a Hungarian mathematician, working in set theory, especially combinatorial set theory. Komjáth is a professor at the Faculty of Sciences of the Eötvös Loránd University. He is currently a visiting faculty member at Emory University in the department of Mathematics and Computer Science. Komjáth won a gold medal at the International Mathematical Olympiad in 1971. His Ph.D. advisor at Eötvös was András Hajnal, and he has two joint papers with Paul Erdős. He received the Paul Erdős Prize in 1990. He is a member of the Hungarian Academy of Sciences. Selected publications * Komjáth, Péter and Vilmos Totik Vilmos Totik (Mosonmagyaróvár, March 8, 1954) is a Hungarians, Hungarian mathematician, working in classical analysis, harmonic analysis, orthogonal polynomials, approximation theory, potential theory. He is a professor of the University of Szege ...: ''Problems and Theorems in Classical Set Theory'', Springer-Verlag, Berlin, 2006. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
György Elekes
György Elekes (19 May 1949 – 29 September 2008) was a Hungarian mathematician and computer scientist who specialized in Combinatorial geometry and Combinatorial set theory. He may be best known for his work in the field that would eventually be called Additive Combinatorics. Particularly notable was his "ingenious" application of the Szemerédi–Trotter theorem to improve the best known lower bound for the sum-product problem. He also proved that any polynomial-time algorithm approximating the volume of convex bodies must have a multiplicative error, and the error grows exponentially on the dimension. With Micha Sharir he set up a framework which eventually led Guth and Katz to the solution of the Erdős distinct distances problem.20.99''n''vol(''K''). That is, any polynomial-time estimator of volume over ''K'' must be inaccurate by at least an exponential factor. Not long before his death he developed new tools in Algebraic geometry and used them to obtain results in Dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
