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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] |
Hypergeometric Identity
In mathematics, hypergeometric identities are equalities involving sums over hypergeometric terms, i.e. the coefficients occurring in hypergeometric series. These Identity (mathematics), identities occur frequently in solutions to combinatorial problems, and also in the analysis of algorithms. These identities were traditionally found 'by hand'. There exist now several algorithms which can find and ''prove'' all hypergeometric identities. Examples : \sum_^ = 2^ : \sum_^ ^2 = : \sum_^ k = n2^ : \sum_^ i = (n+1)- Definition There are two definitions of hypergeometric terms, both used in different cases as explained below. See also hypergeometric series. A term ''tk'' is a hypergeometric term if : \frac is a rational function in ''k''. A term ''F(n,k)'' is a hypergeometric term if : \frac is a rational function in ''k''. There exist two types of sums over hypergeometric terms, the definite and indefinite sums. A definite sum is of the form : \sum_ t_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Q-series
In mathematical area of combinatorics, the ''q''-Pochhammer symbol, also called the ''q''-shifted factorial, is the product (a;q)_n = \prod_^ (1-aq^k)=(1-a)(1-aq)(1-aq^2)\cdots(1-aq^), with (a;q)_0 = 1. It is a ''q''-analog of the Pochhammer symbol (x)_n = x(x+1)\dots(x+n-1), in the sense that \lim_ \frac = (x)_n. The ''q''-Pochhammer symbol is a major building block in the construction of ''q''-analogs; for instance, in the theory of basic hypergeometric series, it plays the role that the ordinary Pochhammer symbol plays in the theory of generalized hypergeometric series. Unlike the ordinary Pochhammer symbol, the ''q''-Pochhammer symbol can be extended to an infinite product: (a;q)_\infty = \prod_^ (1-aq^k). This is an analytic function of ''q'' in the interior of the unit disk, and can also be considered as a formal power series in ''q''. The special case \phi(q) = (q;q)_\infty=\prod_^\infty (1-q^k) is known as Euler's function, and is important in combinatorics, number theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilf–Zeilberger Pair
In mathematics, specifically combinatorics, a Wilf–Zeilberger pair, or WZ pair, is a pair of functions that can be used to certify certain combinatorial identities. WZ pairs are named after Herbert S. Wilf and Doron Zeilberger, and are instrumental in the evaluation of many sums involving binomial coefficients, factorials, and in general any hypergeometric series. A function's WZ counterpart may be used to find an equivalent and much simpler sum. Although finding WZ pairs by hand is impractical in most cases, Gosper's algorithm provides a sure method to find a function's WZ counterpart, and can be implemented in a symbolic manipulation program. Definition Two functions ''F'' and ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MacMahon Master Theorem
In mathematics, MacMahon's master theorem (MMT) is a result in enumerative combinatorics and linear algebra. It was discovered by Percy MacMahon and proved in his monograph ''Combinatory analysis'' (1916). It is often used to derive binomial identities, most notably Dixon's identity. Background In the monograph, MacMahon found so many applications of his result, he called it "a master theorem in the Theory of Permutations." He explained the title as follows: "a Master Theorem from the masterly and rapid fashion in which it deals with various questions otherwise troublesome to solve." The result was re-derived (with attribution) a number of times, most notably by I. J. Good who derived it from his multilinear generalization of the Lagrange inversion theorem. MMT was also popularized by Carlitz who found an exponential power series version. In 1962, Good found a short proof of Dixon's identity from MMT. In 1969, Cartier and Foata found a new proof of MMT by combining alg ... [...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] |
Herbert Wilf
Herbert Saul Wilf (June 13, 1931 – January 7, 2012) was a mathematician, specializing in combinatorics and graph theory. He was the Thomas A. Scott Professor of Mathematics in Combinatorial Analysis and Computing at the University of Pennsylvania. He wrote numerous books and research papers. Together with Neil Calkin he founded ''The Electronic Journal of Combinatorics'' in 1994 and was its editor-in-chief until 2001. Biography Wilf was the author of numerous papers and books, and was adviser and mentor to many students and colleagues. His collaborators include Doron Zeilberger and Donald Knuth. One of Wilf's former students is Richard Garfield, the creator of the collectible card game ''Magic: The Gathering''. He also served as a thesis advisor for E. Roy Weintraub in the late 1960s. Wilf died of a progressive neuromuscular disease in 2012. Awards In 1998, Wilf and Zeilberger received the Leroy P. Steele Prize for Seminal Contribution to Research for their joint pap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Old AT&T
AT&T Corporation, originally the American Telephone and Telegraph Company, is the subsidiary of AT&T Inc. that provides voice, video, data, and Internet telecommunications and professional services to businesses, consumers, and government agencies. During the Bell System's long history, AT&T was at times the world's largest telephone company, the world's largest cable television operator, and a regulated monopoly. At its peak in the 1950s and 1960s, it employed one million people and its revenue ranged between US$3 billion in 1950 ($ in present-day terms) and $12 billion in 1966 ($ in present-day terms). In 2005, AT&T was purchased by Baby Bell and former subsidiary SBC Communications for more than $16 billion ($ in present-day terms). SBC then changed its name to AT&T Inc. Today, AT&T Corporation continues to exist as the long distance subsidiary of AT&T Inc., and its name occasionally shows up in AT&T press releases. Buildings with AT&T logo * AT&T Huro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hebrew Language
Hebrew (; ; ) is a Northwest Semitic language of the Afroasiatic language family. Historically, it is one of the spoken languages of the Israelites and their longest-surviving descendants, the Jews and Samaritans. It was largely preserved throughout history as the main liturgical language of Judaism (since the Second Temple period) and Samaritanism. Hebrew is the only Canaanite language still spoken today, and serves as the only truly successful example of a dead language that has been revived. It is also one of only two Northwest Semitic languages still in use, with the other being Aramaic. The earliest examples of written Paleo-Hebrew date back to the 10th century BCE. Nearly all of the Hebrew Bible is written in Biblical Hebrew, with much of its present form in the dialect that scholars believe flourished around the 6th century BCE, during the time of the Babylonian captivity. For this reason, Hebrew has been referred to by Jews as '' Lashon Hakodesh'' (, ) since an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wired (magazine)
''Wired'' (stylized as ''WIRED'') is a monthly American magazine, published in print and online editions, that focuses on how emerging technologies affect culture, the economy, and politics. Owned by Condé Nast, it is headquartered in San Francisco, California, and has been in publication since March/April 1993. Several spin-offs have been launched, including '' Wired UK'', ''Wired Italia'', ''Wired Japan'', and ''Wired Germany''. From its beginning, the strongest influence on the magazine's editorial outlook came from founding editor and publisher Louis Rossetto. With founding creative director John Plunkett, Rossetto in 1991 assembled a 12-page prototype, nearly all of whose ideas were realized in the magazine's first several issues. In its earliest colophons, ''Wired'' credited Canadian media theorist Marshall McLuhan as its "patron saint". ''Wired'' went on to chronicle the evolution of digital technology and its impact on society. ''Wired'' quickly became recognized ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New Scientist
''New Scientist'' is a magazine covering all aspects of science and technology. Based in London, it publishes weekly English-language editions in the United Kingdom, the United States and Australia. An editorially separate organisation publishes a monthly Dutch-language edition. First published on 22 November 1956, ''New Scientist'' has been available in online form since 1996. Sold in retail outlets (paper edition) and on subscription (paper and/or online), the magazine covers news, features, reviews and commentary on science, technology and their implications. ''New Scientist'' also publishes speculative articles, ranging from the technical to the philosophical. ''New Scientist'' was acquired by Daily Mail and General Trust (DMGT) in March 2021. History Ownership The magazine was founded in 1956 by Tom Margerison, Max Raison and Nicholas Harrison as ''The New Scientist'', with Issue 1 on 22 November 1956, priced at one shilling (a twentieth of a pound in pre-decimal UK cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ultrafinitism
In the philosophy of mathematics, ultrafinitism (also known as ultraintuitionism,International Workshop on Logic and Computational Complexity, ''Logic and Computational Complexity'', Springer, 1995, p. 31. strict formalism,St. Iwan (2000),On the Untenability of Nelson's Predicativism, ''Erkenntnis'' 53(1–2), pp. 147–154. strict finitism, actualism, predicativism, and strong finitism) is a form of finitism and intuitionism. There are various philosophies of mathematics that are called ultrafinitism. A major identifying property common among most of these philosophies is their objections to total function, totality of number theoretic functions like exponentiation over natural numbers. Main ideas Like other finitism, finitists, ultrafinitists deny the existence of the infinite set N of natural numbers, i.e. there is a largest natural number. In addition, some ultrafinitists are concerned with acceptance of objects in mathematics that no one can construct in practice because of p ... [...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, mathematical analysis, 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 Ramanujan's lost notebook, Lost Notebook. He is highly interested in mathematical pedagogy. His book ''The Theory of Partitions'' is the standard reference on the subject of integer par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
