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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] |
Integer Partition
In number theory and combinatorics, a partition of a positive integer , also called an integer partition, is a way of writing as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. (If order matters, the sum becomes a composition.) For example, can be partitioned in five distinct ways: : : : : : The order-dependent composition is the same partition as , and the two distinct compositions and represent the same partition as . A summand in a partition is also called a part. The number of partitions of is given by the partition function . So . The notation means that is a partition of . Partitions can be graphically visualized with Young diagrams or Ferrers diagrams. They occur in a number of branches of mathematics and physics, including the study of symmetric polynomials and of the symmetric group and in group representation theory in general. Examples The seven partitions of 5 are: * 5 * 4 + 1 * 3 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doron Zeilberger
Doron Zeilberger (דורון ציילברגר, born 2 July 1950 in Haifa, Israel) is an Israeli 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. Contributions Zeilberger has made contributions to combinatorics, hypergeometric identities, and q-series. Zeilberger 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 ... [...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 conject ... [...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 |
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: * |
John Stembridge
John Stembridge is a Professor of Mathematics at University of Michigan. He received his Ph.D. from Massachusetts Institute of Technology in 1985 under the direction of Richard P. Stanley. His dissertation was called ''Combinatorial Decompositions of Characters of SL''(''n,C''). 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 List of Guggenheim Fellowships awarded in 2000, in 2000 for work in ''Combinatorial aspects of root systems and Weyl characters.''. He has written Maple (software), Maple packages that can be used for computing symmetric functions, posets, root systems, and finite ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David P
David (; , "beloved one") (traditional spelling), , ''Dāwūd''; grc-koi, Δαυΐδ, Dauíd; la, Davidus, David; gez , ዳዊት, ''Dawit''; xcl, Դաւիթ, ''Dawitʿ''; cu, Давíдъ, ''Davidŭ''; possibly meaning "beloved one". was, according to the Hebrew Bible, the third king of the United Kingdom of Israel. In the Books of Samuel, he is described as a young shepherd and harpist who gains fame by slaying Goliath, a champion of the Philistines, in southern Canaan. David becomes a favourite of Saul, the first king of Israel; he also forges a notably close friendship with Jonathan, a son of Saul. However, under the paranoia that David is seeking to usurp the throne, Saul attempts to kill David, forcing the latter to go into hiding and effectively operate as a fugitive for several years. After Saul and Jonathan are both killed in battle against the Philistines, a 30-year-old David is anointed king over all of Israel and Judah. Following his rise to power, David ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
