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Plane Partition
In mathematics and especially in combinatorics, a plane partition is a two-dimensional array of nonnegative integers \pi_ (with positive number, positive integer indices ''i'' and ''j'') that is nonincreasing in both indices. This means that : \pi_ \ge \pi_ and \pi_ \ge \pi_ for all ''i'' and ''j''. Moreover, only finitely many of the \pi_ may be nonzero. Plane partitions are a generalization of Partition (number theory), partitions of an integer. A plane partition may be represented visually by the placement of a stack of \pi_ unit cubes above the point (''i'', ''j'') in the plane, giving a three-dimensional solid as shown in the picture. The image has matrix form : \begin 4 & 4 & 3 & 2 & 1\\ 4 & 3 & 1 & 1\\ 3 & 2 & 1\\ 1 \end Plane partitions are also often described by the positions of the unit cubes. From this point of view, a plane partition can be defined as a finite subset \mathcal of positive integer lattice points (''i'', ''j'', ''k'') in \mathbb^3, such that if (''r'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ian G
Ian or Iain is a name of Scottish Gaelic origin, which is derived from the Hebrew given name ( Yohanan, ') and corresponds to the English name John. The spelling Ian is an Anglicization of the Scottish Gaelic forename ''Iain''. This name is a popular name in Scotland, where it originated, as well as in other English-speaking countries. The name has fallen out of the top 100 male baby names in the United Kingdom, having peaked in popularity as one of the top 10 names throughout the 1960s. In 1900, Ian ranked as the 180th most popular male baby name in England and Wales. , the name has been in the top 100 in the United States every year since 1982, peaking at 65 in 2003. Other Gaelic forms of the name "John" include " Seonaidh" ("Johnny" from Lowland Scots), "Seon" (from English), "Seathan", and "Seán" and "Eoin" (from Irish). The Welsh equivalent is Ioan, the Cornish counterpart is Yowan and the Breton equivalent is Yann. Notable people named Ian Given name * Ian Ago ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doron Zeilberger
Doron Zeilberger (; born 2 July 1950) is an Israeli-American mathematician, known for his work in combinatorics. Education and career He received his doctorate from the Weizmann Institute of Science in 1976, under the direction of Harry Dym, with the thesis "New Approaches and Results in the Theory of Discrete Analytic Functions." He is a Board of Governors Professor of Mathematics at Rutgers University. Mathematical work Zeilberger has made contributions to combinatorics, hypergeometric identities, and q-series. He gave the first proof of the alternating sign matrix conjecture, noteworthy not only for its mathematical content, but also for the fact that Zeilberger recruited nearly a hundred volunteer checkers to "pre-referee" the paper. In 2011, together with Manuel Kauers and Christoph Koutschan, Zeilberger proved the ''q''-TSPP conjecture, which was independently stated in 1983 by George Andrews and David P. Robbins. Zeilberger is an ultrafinitist. He is also known ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manuel Kauers
Manuel Kauers (born 20 February 1979 in Lahnstein, West Germany) is a German mathematician and computer scientist. He is working on computer algebra and its applications to discrete mathematics. He is currently professor for algebra at Johannes Kepler University (JKU) in Linz, Austria, and leader of the Institute for Algebra at JKU. Before that, he was affiliated with that university's Research Institute for Symbolic Computation (RISC). Kauers studied computer science at the University of Karlsruhe in Germany from 1998 to 2002 and then moved to RISC, where he completed his PhD in symbolic computation in 2005 under the supervision of Peter Paule. He earned his habilitation in mathematics from JKU in 2008. Together with Doron Zeilberger and Christoph Koutschan, Kauers proved two famous open conjectures in combinatorics using large scale computer algebra calculations. Both proofs appeared in the Proceedings of the National Academy of Sciences. The first concerned a conjectu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christoph Koutschan
Christoph Koutschan is a German mathematician and computer scientist. He is currently with the Johann Radon Institute for Computational and Applied Mathematics (RICAM) of the Austrian Academy of Sciences. Education Christoph Koutschan (born 12 December 1978 in Dillingen an der Donau, Germany) is a German mathematician and computer scientist. He studied computer science at the University of Erlangen-Nuremberg in Germany from 1999 to 2005 and then moved to the Research Institute for Symbolic Computation (RISC) in Linz, Austria, where he completed his PhD in symbolic computation in 2009 under the supervision of Peter Paule. Career Koutschan is working on computer algebra, particularly on holonomic functions, with applications to combinatorics, special functions, knot theory, and physics. Together with Doron Zeilberger and Manuel Kauers, Koutschan proved two famous open conjectures in combinatorics using large scale computer algebra calculations. Both proofs appeared in the Pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Paule
Peter Paule is an Austrian mathematician who works in symbolic computation and its connections to combinatorics, number theory, and special functions. Since 1990 he has held a faculty position at the Research Institute for Symbolic Computation of the Johannes Kepler University of Linz, and since 2009 he has directed the Institute.Curriculum vitae retrieved 2015-01-15. Paule earned his doctorate from the in 1982 under the supervision of Johann Cigler, and earned a from Johannes Kepler University in 1996. He is a member of the [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Advances In Mathematics
''Advances in Mathematics'' is a peer-reviewed scientific journal covering research on pure mathematics. It was established in 1961 by Gian-Carlo Rota. The journal publishes 18 issues each year, in three volumes. At the origin, the journal aimed at publishing articles addressed to a broader "mathematical community", and not only to mathematicians in the author's field. Herbert Busemann writes, in the preface of the first issue, "The need for expository articles addressing either all mathematicians or only those in somewhat related fields has long been felt, but little has been done outside of the USSR. The serial publication ''Advances in Mathematics'' was created in response to this demand." Abstracting and indexing The journal is abstracted and indexed in: * [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Stembridge
John Stembridge is a Professor of Mathematics at the University of Michigan. He received his Ph.D. from the Massachusetts Institute of Technology in 1985 under the direction of Richard P. Stanley. His dissertation was entitled ''Combinatorial Decompositions of Characters of SL''(''n,C''). He has had 8 Ph.D. students. He is one of the participants in the Atlas of Lie Groups and Representations. Research His research interests are in combinatorics, with particular emphasis on the following areas: *Topics related to algebra, especially representation theory *Coxeter groups and root systems *Enumerative combinatorics *Symmetric functions *Hypergeometric series and q-series *Computational problems and algorithms in algebra He was awarded a Guggenheim Fellowship in 2000 for work in ''Combinatorial aspects of root systems and Weyl characters.''. He has written Maple packages that can be used for computing symmetric functions, posets, root systems, and finite Coxeter group In math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David P
David (; , "beloved one") was a king of ancient Israel and Judah and the third king of the United Monarchy, according to the Hebrew Bible and Old Testament. The Tel Dan stele, an Aramaic-inscribed stone erected by a king of Aram-Damascus in the late 9th/early 8th centuries BCE to commemorate a victory over two enemy kings, contains the phrase (), which is translated as " House of David" by most scholars. The Mesha Stele, erected by King Mesha of Moab in the 9th century BCE, may also refer to the "House of David", although this is disputed. According to Jewish works such as the '' Seder Olam Rabbah'', '' Seder Olam Zutta'', and ''Sefer ha-Qabbalah'' (all written over a thousand years later), David ascended the throne as the king of Judah in 885 BCE. Apart from this, all that is known of David comes from biblical literature, the historicity of which has been extensively challenged,Writing and Rewriting the Story of Solomon in Ancient Israel; by Isaac Kalimi; page 32; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Andrews (mathematician)
George Eyre Andrews (born December 4, 1938) is an American mathematician working in special functions, number theory, analysis and combinatorics. Education and career He is currently an Evan Pugh Professor of Mathematics at Pennsylvania State University. He did his undergraduate studies at Oregon State University and received his PhD in 1964 at the University of Pennsylvania where his advisor was Hans Rademacher. During 2008–2009 he was president of the American Mathematical Society. Contributions Andrews's contributions include several monographs and over 250 research and popular articles on q-series, special functions, combinatorics and applications. He is considered to be the world's leading expert in the theory of integer partitions. In 1976 he discovered Ramanujan's Lost Notebook. He is interested in mathematical pedagogy. His book ''The Theory of Partitions'' is the standard reference on the subject of integer partitions. He has advanced mathematics in the theories o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
