Related Research Articles
Freeman John Dyson was an English-American theoretical physicist and mathematician known for his works in quantum field theory, astrophysics, random matrices, mathematical formulation of quantum mechanics, condensed matter physics, nuclear physics, and engineering. He was Professor Emeritus in the Institute for Advanced Study in Princeton and a member of the Board of Sponsors of the Bulletin of the Atomic Scientists.
Sir Michael Francis Atiyah was a British-Lebanese mathematician specialising in geometry. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004.
Robert Phelan Langlands, is a Canadian mathematician. He is best known as the founder of the Langlands program, a vast web of conjectures and results connecting representation theory and automorphic forms to the study of Galois groups in number theory, for which he received the 2018 Abel Prize. He was an emeritus professor and occupied Albert Einstein's office at the Institute for Advanced Study in Princeton, until 2020 when he retired.
In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. For example, 4 can be partitioned in five distinct ways:
In graph theory, an isomorphism of graphsG and H is a bijection between the vertex sets of G and H
The Oersted Medal recognizes notable contributions to the teaching of physics. Established in 1936, it is awarded by the American Association of Physics Teachers. The award is named for Hans Christian Ørsted. It is the Association's most prestigious award.
Karl Mahlburg is an American mathematician whose research interests lie in the areas of modular forms, partitions, combinatorics and number theory.
In graph theory, the Dulmage–Mendelsohn decomposition is a partition of the vertices of a bipartite graph into subsets, with the property that two adjacent vertices belong to the same subset if and only if they are paired with each other in a perfect matching of the graph. It is named after A. L. Dulmage and Nathan Mendelsohn, who published it in 1958. A generalization to any graph is the Edmonds–Gallai decomposition, using the Blossom algorithm.
George Eyre Andrews is an American mathematician working in special functions, number theory, analysis and combinatorics.
Jack R. Edmonds is an American-born and educated computer scientist and mathematician who lived and worked in Canada for much of his life. He has made fundamental contributions to the fields of combinatorial optimization, polyhedral combinatorics, discrete mathematics and the theory of computing. He was the recipient of the 1985 John von Neumann Theory Prize.
Eureka is a journal published annually by The Archimedeans, the Mathematical Society of Cambridge University. It is one of the oldest recreational mathematics publications still in existence. Eureka includes many mathematical articles on a variety different topics – written by students and mathematicians from all over the world – as well as a short summary of the activities of the society, problem sets, puzzles, artwork and book reviews.
In combinatorial mathematics, a Dowling geometry, named after Thomas A. Dowling, is a matroid associated with a group. There is a Dowling geometry of each rank for each group. If the rank is at least 3, the Dowling geometry uniquely determines the group. Dowling geometries have a role in matroid theory as universal objects ; in that respect they are analogous to projective geometries, but based on groups instead of fields.
In mathematics, Ramanujan's congruences are some remarkable congruences for the partition function p(n). The mathematician Srinivasa Ramanujan discovered the congruences
Ken Ono is a Japanese-American mathematician who specializes in number theory, especially in integer partitions, modular forms, umbral moonshine, the Riemann Hypothesis and the fields of interest to Srinivasa Ramanujan. He is the Asa Griggs Candler Professor of Mathematics at Emory University and the Thomas Jefferson Professor of Mathematics at the University of Virginia. He served as the Vice President of the American Mathematical Society from 2018 to 2021.
In mathematics the Selberg integral is a generalization of Euler beta function to n dimensions introduced by Atle Selberg (1944).
In mathematics, the Dyson conjecture is a conjecture about the constant term of certain Laurent polynomials, proved independently in 1962 by Wilson and Gunson. Andrews generalized it to the q-Dyson conjecture, proved by Zeilberger and Bressoud and sometimes called the Zeilberger–Bressoud theorem. Macdonald generalized it further to more general root systems with the Macdonald constant term conjecture, proved by Cherednik.
Verena Esther Huber-Dyson was a Swiss-American mathematician, known for work in group theory and formal logic. She has been described as a "brilliant mathematician", and did research on the interface between algebra and logic, focusing on undecidability in group theory. At the time of her death, she was emeritus faculty in the philosophy department of the University of Calgary, Alberta.
In mathematics, the crank conjecture was a conjecture about the existence of the crank of a partition that separates partitions of a number congruent to 6 mod 11 into 11 equal classes. The conjecture was introduced by Dyson (1944) and proved by Andrews and Garvan (1987).
In mathematics, particularly in the fields of number theory and combinatorics, the rank of a partition of a positive integer is a certain integer associated with the partition. In fact at least two different definitions of rank appear in the literature. The first definition, with which most of this article is concerned, is that the rank of a partition is the number obtained by subtracting the number of parts in the partition from the largest part in the partition. The concept was introduced by Freeman Dyson in a paper published in the journal Eureka. It was presented in the context of a study of certain congruence properties of the partition function discovered by the Indian mathematical genius Srinivasa Ramanujan. A different concept, sharing the same name, is used in combinatorics, where the rank is taken to be the size of the Durfee square of the partition.
In number theory, the crank of a partition of an integer is a certain integer associated with the partition. The term was first introduced without a definition by Freeman Dyson in a 1944 paper published in Eureka, a journal published by the Mathematics Society of Cambridge University. Dyson then gave a list of properties this yet-to-be-defined quantity should have. In 1988, George E. Andrews and Frank Garvan discovered a definition for the crank satisfying the properties hypothesized for it by Dyson.
References
- ↑ "CURRICULUM VITAE: Francis G. Garvan" (PDF). qseries.org. 18 July 2016. Retrieved 7 April 2019.
- ↑ "George Andrews' Students". sites.math.rutgers.edu. Retrieved 7 April 2019.
- ↑ Garvan, Francis G. (May 1986). "1". Generalizations of Dyson's rank (Thesis). Retrieved 22 March 2019.
- ↑ Garvan, Francis G. "Frank Garvan: List of Publications" . Retrieved 22 March 2019.
- ↑ Askey, Richard (1999). "The work of George Andrews: a Madison perspective" (PDF). Séminaire Lotharingien de Combinatoire. 42: Art. B42b, 24pp. MR 1701581.
- ↑ Dyson, Freeman J. (1944). "Some Guesses in The Theory of Partitions". Eureka (Cambridge). 8: 10–15. ISBN 9780821805619.
