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Endre Boros
Endre Boros (born 21 September 1953) is a Hungarian-American mathematician, a Distinguished Professor at Rutgers University in New Brunswick, New Jersey, and the Director of the Center for Operations Research (RUTCOR). He is the author of 15 book chapters and edited volumes, and 165 research papers. He is Associate Editor of the Annals of Mathematics and Artificial Intelligence, and Editor-in-Chief of both the Annals of Operations Research and Discrete Applied Mathematics. Results settled a conjecture by Beniamino Segre about the cyclic structure of finite projective planes, and provided the best known bound for a question posed by Paul Erdős about blocking sets of Galois planes. proved that perfect graph In graph theory, a perfect graph is a Graph (discrete mathematics), graph in which the Graph coloring, chromatic number equals the size of the maximum clique, both in the graph itself and in every induced subgraph. In all graphs, the chromatic nu ...s are kernel solvable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rutgers University
Rutgers University ( ), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of three campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's College and was affiliated with the Reformed Church in America, Dutch Reformed Church. It is the eighth-oldest college in the United States, the second-oldest in New Jersey (after Princeton University), and one of nine colonial colleges that were chartered before the American Revolution.Stoeckel, Althea"Presidents, professors, and politics: the colonial colleges and the American revolution", ''Conspectus of History'' (1976) 1(3):45–56. In 1825, Queen's College was renamed Rutgers College in honor of Colonel Henry Rutgers, whose substantial gift to the school had stabilized its finances during a period of uncertainty. For most of its existence, Rutgers was a Private university, private liberal arts college. It has evolved into a Mixed-sex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beniamino Segre
Beniamino Segre (16 February 1903 – 2 October 1977) was an Italian mathematician who is remembered today as a major contributor to algebraic geometry and one of the founders of finite geometry. Life and career He was born and studied in Turin. Corrado Segre, his uncle, also served as his doctoral advisor. Among his main contributions to algebraic geometry are studies of birational invariants of algebraic varieties, singularities and algebraic surfaces. His work was in the style of the old Italian School, although he also appreciated the greater rigour of modern algebraic geometry. Segre was a pioneer in finite geometry, in particular projective geometry based on vector spaces over a finite field. In a well-known paper he proved the following theorem: In a Desarguesian plane of odd order, the ovals are exactly the irreducible conics. In 1959 he authored a survey "Le geometrie di Galois" on Galois geometry. According to J. W. P. Hirschfeld, it "gave a comprehensive list of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Projective Plane
In mathematics, a projective plane is a geometric structure that extends the concept of a plane (geometry), plane. In the ordinary Euclidean plane, two lines typically intersect at a single point, but there are some pairs of lines (namely, parallel lines) that do not intersect. A projective plane can be thought of as an ordinary plane equipped with additional "points at infinity" where parallel lines intersect. Thus ''any'' two distinct lines in a projective plane intersect at exactly one point. Renaissance artists, in developing the techniques of drawing in Perspective (graphical)#Renaissance, perspective, laid the groundwork for this mathematical topic. The archetypical example is the real projective plane, also known as the extended Euclidean plane. This example, in slightly different guises, is important in algebraic geometry, topology and projective geometry where it may be denoted variously by , RP2, or P2(R), among other notations. There are many other projective planes, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Erdős
Paul Erdős ( ; 26March 191320September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, graph theory, number theory, mathematical analysis, approximation theory, set theory, and probability theory. Much of his work centered on discrete mathematics, cracking many previously unsolved problems in the field. He championed and contributed to Ramsey theory, which studies the conditions in which order necessarily appears. Overall, his work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics. Erdős published around 1,500 mathematical papers during his lifetime, a figure that remains unsurpassed. He was known both for his social practice of mathematics, working with more than 500 collaborators, and for his eccentric lifestyle; ''Time'' magazine called him "The Oddball's Oddba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Graph
In graph theory, a perfect graph is a Graph (discrete mathematics), graph in which the Graph coloring, chromatic number equals the size of the maximum clique, both in the graph itself and in every induced subgraph. In all graphs, the chromatic number is greater than or equal to the size of the maximum clique, but they can be far apart. A graph is perfect when these numbers are equal, and remain equal after the deletion of arbitrary subsets of vertices. The perfect graphs include many important families of graphs and serve to unify results relating Graph coloring, colorings and cliques in those families. For instance, in all perfect graphs, the graph coloring problem, maximum clique problem, and maximum independent set problem can all be solved in polynomial time, despite their greater complexity for non-perfect graphs. In addition, several important minimax theorems in combinatorics, including Dilworth's theorem and Mirsky's theorem on partially ordered sets, Kőnig's theorem (gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Graph Theorem
In graph theory, the perfect graph theorem of states that an undirected graph is perfect if and only if its complement graph is also perfect. This result had been conjectured by , and it is sometimes called the weak perfect graph theorem to distinguish it from the strong perfect graph theorem characterizing perfect graphs by their forbidden induced subgraphs. Statement A perfect graph is an undirected graph with the property that, in every one of its induced subgraphs, the size of the largest clique equals the minimum number of colors in a coloring of the subgraph. Perfect graphs include many important graphs classes including bipartite graphs, chordal graphs, and comparability graphs. The complement of a graph has an edge between two vertices if and only if the original graph does not have an edge between the same two vertices. Thus, a clique in the original graph becomes an independent set in the complement and a coloring of the original graph becomes a clique cover of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flow Network
In graph theory, a flow network (also known as a transportation network) is a directed graph where each edge has a capacity and each edge receives a flow. The amount of flow on an edge cannot exceed the capacity of the edge. Often in operations research, a directed graph is called a network, the vertices are called nodes and the edges are called arcs. A flow must satisfy the restriction that the amount of flow into a node equals the amount of flow out of it, unless it is a source, which has only outgoing flow, or sink, which has only incoming flow. A flow network can be used to model traffic in a computer network, circulation with demands, fluids in pipes, currents in an electrical circuit, or anything similar in which something travels through a network of nodes. As such, efficient algorithms for solving network flows can also be applied to solve problems that can be reduced to a flow network, including survey design, airline scheduling, image segmentation, and the matching prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horn Function
In the theory of special functions in mathematics, the Horn functions (named for Jakob Horn) are the 34 distinct convergent hypergeometric series In mathematics, the Gaussian or ordinary hypergeometric function 2''F''1(''a'',''b'';''c'';''z'') is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is ... of order two (i.e. having two independent variables), enumerated by (corrected by ). They are listed in . B. C. Carlson revealed a problem with the Horn function classification scheme. The total 34 Horn functions can be further categorised into 14 complete hypergeometric functions and 20 confluent hypergeometric functions. The complete functions, with their domain of convergence, are: * F_1(\alpha;\beta,\beta';\gamma;z,w)\equiv\sum_^\sum_^\frac\frac/;, z, <1\land, w, <1 * * |
Combinatorica
''Combinatorica'' is an international journal of mathematics, publishing papers in the fields of combinatorics and computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, .... It started in 1981, with László Babai and László Lovász as the editors-in-chief with Paul Erdős as honorary editor-in-chief. The current editors-in-chief are Imre Bárány and József Solymosi. The advisory board consists of Ronald Graham, Gyula O. H. Katona, Miklós Simonovits, Vera Sós, and Endre Szemerédi. It is published by the János Bolyai Mathematical Society and Springer Verlag. The following members of the '' Hungarian School of Combinatorics'' have strongly contributed to the journal as authors, or have served as editors: Miklós Ajtai, László Babai, József Beck, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Mathematics (journal)
''Discrete Mathematics'' is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications. It was established in 1971 and is published by North-Holland Publishing Company. It publishes both short notes, full length contributions, as well as survey articles. In addition, the journal publishes a number of special issues each year dedicated to a particular topic. Although originally it published articles in French and German, it now allows only English language articles. The editor-in-chief is Douglas West ( University of Illinois, Urbana). History The journal was established in 1971. The first article it published was written by Paul Erdős, who went on to publish a total of 84 papers in the journal. Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor The impact factor (IF) or journal impact facto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete & Computational Geometry
'' Discrete & Computational Geometry'' is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986 by Jacob E. Goodman and Richard M. Pollack, the journal publishes articles on discrete geometry and computational geometry. Abstracting and indexing The journal is indexed in: * ''Mathematical Reviews'' * '' Zentralblatt MATH'' * ''Science Citation Index'' * ''Current Contents ''Current Contents'' is a rapid alerting service database from Clarivate, formerly the Institute for Scientific Information and Thomson Reuters. It is published online and in several different printed subject sections. History ''Current Contents ...'' Notable articles Two articles published in ''Discrete & Computational Geometry'', one by Gil Kalai in 1992 with a proof of a subexponential upper bound on the diameter of a polytope and another by Samuel Ferguson in 2006 on the Kepler conjecture on optimal three-dimensional sphere packing, earned their authors the Fulk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1953 Births
Events January * January 6 – The Asian Socialist Conference opens in Rangoon, Burma. * January 12 – Estonian émigrés found a government-in-exile in Oslo. * January 14 ** Marshal Josip Broz Tito is chosen President of Yugoslavia. ** The CIA-sponsored Robertson Panel first meets to discuss the UFO phenomenon. * January 15 ** Georg Dertinger, foreign minister of East Germany, is arrested for spying. ** British security forces in West Germany arrest 7 members of the Naumann Circle, a clandestine Neo-Nazi organization. * January 19 – 71.1% of all television sets in the United States are tuned into '' I Love Lucy'', to watch Lucy give birth to Little Ricky, which is more people than those who tune into Dwight Eisenhower's inauguration the next day. This record is never broken. * January 24 ** Mau Mau Uprising: Rebels in Kenya kill the Ruck family (father, mother, and six-year-old son). ** Leader of East Germany Walter Ulbricht announces that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
