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Turán's Brick Factory Problem
In the mathematics of graph drawing, Turán's brick factory problem asks for the minimum number of crossings in a drawing of a complete bipartite graph. The problem is named after Pál Turán, who formulated it while being forced to work in a brick factory during World War II. A drawing method found by Kazimierz Zarankiewicz has been conjectured to give the correct answer for every complete bipartite graph, and the statement that this is true has come to be known as the Zarankiewicz crossing number conjecture. The conjecture remains open, with only some special cases solved. Origin and formulation During World War II, Hungarian mathematician Pál Turán was forced to work in a brick factory, pushing wagon loads of bricks from kilns to storage sites. The factory had tracks from each kiln to each storage site, and the wagons were harder to push at the points where tracks crossed each other. Turán was inspired by this situation to ask how the factory might be redesigned to mini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zarankiewicz K4 7
Kazimierz Zarankiewicz (2 May 1902 – 5 September 1959) was a Polish mathematician and Professor at the Warsaw University of Technology who was interested primarily in topology and graph theory. Biography Zarankiewicz was born in Częstochowa. He studied at the University of Warsaw, together with Zygmunt Janiszewski, Stefan Mazurkiewicz, Wacław Sierpiński, Kazimierz Kuratowski, and Stanisław Saks. During World War II, Zarankiewicz took part in illegal teaching, forbidden by the German authorities, and eventually was sent to a concentration camp. He survived and became a teacher at Warsaw University of Technology. He visited universities in Tomsk, Harvard, London, and Vienna. He served as president of the Warsaw section of the Polish Mathematical Society and the International Astronautical Federation. He died in London, England. Research contributions Zarankiewicz wrote works on cut-points in connected spaces, on conformal mappings, on complex functions and number theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gerhard Ringel
Gerhard Ringel (October 28, 1919 in Kollnbrunn, Austria – June 24, 2008 in Santa Cruz, California) was a German mathematician. He was one of the pioneers in graph theory and contributed significantly to the proof of the Heawood conjecture (now the Ringel–Youngs theorem), a mathematical problem closely linked with the four color theorem. Although born in Austria, Ringel was raised in Czechoslovakia and attended Charles University before being drafted into the Wehrmacht in 1940 (after Germany had taken control of much of what had been Czechoslovakia). After the war Ringel served for over four years in a Soviet prisoner of war camp. He earned his PhD from the University of Bonn in 1951 with a thesis written under the supervision of Emanuel Sperner and Ernst Peschl. Ringel started his academic career as professor at the Free University Berlin. In 1970 he left Germany due to bureaucratic consequences of the German student movement, and continued his career at the University ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Problems
A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems. It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox. Real-world problems Informal "real-world" mathematical problems are questions related to a concrete setting, such as "Adam has five apples and gives John three. How many has he left?". Such questions are usually more difficult to solve than regular mathematical exercises like "5 − 3", even if one knows the mathematics required to solve the problem. Known as word problems, they are used in mathematics education to teach students to connect real-world situations to the abstract language of mathematics. In general, to use mathematics for solving a real-world problem, the first ste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Drawing
Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graph (discrete mathematics), graphs arising from applications such as social network analysis, cartography, linguistics, and bioinformatics. A drawing of a graph or network diagram is a pictorial representation of the vertex (graph theory), vertices and edge (graph theory), edges of a graph. This drawing should not be confused with the graph itself: very different layouts can correspond to the same graph., p. 6. In the abstract, all that matters is which pairs of vertices are connected by edges. In the concrete, however, the arrangement of these vertices and edges within a drawing affects its understandability, usability, fabrication cost, and aesthetics. The problem gets worse if the graph changes over time by adding and deleting edges (dynamic graph drawing) and the goal is to preserve the user's menta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Graph Theory
In mathematics, topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological spaces. It also studies immersions of graphs. Embedding a graph in a surface means that we want to draw the graph on a surface, a sphere for example, without two edges intersecting. A basic embedding problem often presented as a mathematical puzzle is the three utilities problem. Other applications can be found in printing electronic circuits where the aim is to print (embed) a circuit (the graph) on a circuit board (the surface) without two connections crossing each other and resulting in a short circuit. Graphs as topological spaces To an undirected graph we may associate an abstract simplicial complex ''C'' with a single-element set per vertex and a two-element set per edge. The geometric realization , ''C'', of the complex consists of a copy of the unit interval ,1per edge, with the endpoints of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fundamenta Mathematicae
''Fundamenta Mathematicae'' is a peer-reviewed scientific journal of mathematics with a special focus on the foundations of mathematics, concentrating on set theory, mathematical logic, topology and its interactions with algebra, and dynamical systems. Originally it only covered topology, set theory, and foundations of mathematics: it was the first specialized journal in the field of mathematics..... It is published by the Mathematics Institute of the Polish Academy of Sciences. History The journal was conceived by Zygmunt Janiszewski as a means to foster mathematical research in Poland.According to and to the introduction to the 100th volume of the journal (1978, pp=1–2). These two sources cite an article written by Janiszewski himself in 1918 and titled "''On the needs of Mathematics in Poland''". Janiszewski required that, in order to achieve its goal, the journal should not force Polish mathematicians to submit articles written exclusively in Polish, and should be devoted ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Graph Theory
The ''Journal of Graph Theory'' is a peer-reviewed mathematics journal specializing in graph theory and related areas, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. It is published by John Wiley & Sons. The journal was established in 1977 by Frank Harary.Frank Harary a biographical sketch at the ACM site The are [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics, Probability And Computing
''Combinatorics, Probability and Computing'' is a peer-reviewed scientific journal in mathematics published by Cambridge University Press. Its editor-in-chief is Béla Bollobás (DPMMS and University of Memphis). History The journal was established by Bollobás in 1992. Fields Medalist Timothy Gowers calls it "a personal favourite" among combinatorics journals and writes that it "maintains a high standard". Content The journal covers combinatorics, probability theory, and theoretical computer science. Currently, it publishes six issues annually. As with other journals from the same publisher, it follows a hybrid green/gold open access policy, in which authors may either place copies of their papers in an institutional repository after a six-month embargo period, or pay an open access charge to make their papers free to read on the journal's website. Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the jou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Electronic Journal Of Combinatorics
The ''Electronic Journal of Combinatorics'' is a peer-reviewed open access scientific journal covering research in combinatorial mathematics. The journal was established in 1994 by Herbert Wilf (University of Pennsylvania) and Neil Calkin ( Georgia Institute of Technology). The Electronic Journal of Combinatorics is a founding member of the Free Journal Network. According to the ''Journal Citation Reports'', the journal had a 2017 impact factor of 0.762. Editors-in-chief Current The current editors-in-chief are: * Maria Axenovich, Karlsruhe Institute of Technology, Germany * Miklós Bóna, University of Florida, United States * Julia Böttcher, London School of Economics, United Kingdom * Richard A. Brualdi, University of Wisconsin, Madison, United States * Eric Fusy, CNRS/LIX, École Polytechnique, France * Catherine Greenhill, UNSW Sydney, Australia * Brendan McKay, Australian National University, Australia * Bojan Mohar, Simon Fraser University, Canada * Marc Noy, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SIAM Journal On Discrete Mathematics
'' SIAM Journal on Discrete Mathematics'' is a peer-reviewed mathematics journal published quarterly by the Society for Industrial and Applied Mathematics (SIAM). The journal includes articles on pure and applied discrete mathematics. It was established in 1988, along with the ''SIAM Journal on Matrix Analysis and Applications'', to replace the ''SIAM Journal on Algebraic and Discrete Methods''. The journal is indexed by ''Mathematical Reviews'' and Zentralblatt MATH. Its 2009 MCQ was 0.57. According to the ''Journal Citation Reports'', the journal has a 2016 impact factor of 0.755. Although its official ISO abbreviation is ''SIAM J. Discrete Math.'', its publisher and contributors frequently use the shorter abbreviation ''SIDMA''. References External links * Combinatorics journals Publications established in 1988 English-language journals Discrete Mathematics Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way ana ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Combinatorial Theory
The ''Journal of Combinatorial Theory'', Series A and Series B, are mathematical journals specializing in combinatorics and related areas. They are published by Elsevier. ''Series A'' is concerned primarily with structures, designs, and applications of combinatorics. ''Series B'' is concerned primarily with graph and matroid theory. The two series are two of the leading journals in the field and are widely known as ''JCTA'' and ''JCTB''. The journal was founded in 1966 by Frank Harary and Gian-Carlo Rota.They are acknowledged on the journals' title pages and Web sites. SeEditorial board of JCTA Originally there was only one journal, which was split into two parts in 1971 as the field grew rapidly. An electronic, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
