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N! conjecture

Index N! conjecture

In mathematics, the n! conjecture is the conjecture that the dimension of a certain bi-graded module of diagonal harmonics is n!. [1]

23 relations: Adriano Garsia, Affine Hecke algebra, Claudio Procesi, Conjecture, Dimension, Hall–Littlewood polynomials, Hilbert scheme, Ian G. Macdonald, Jack function, Journal of the American Mathematical Society, Kostka polynomial, Macdonald polynomials, Mark Haiman, Module (mathematics), Orthogonal polynomials, Representation theory of the symmetric group, Root system, Séminaire Lotharingien de Combinatoire, Schur polynomial, Stochastic matrix, Symmetric function, Symmetric group, Zonal spherical function.

Adriano Garsia

Adriano Mario Garsia (born 20 August 1928) is a Tunisian-born Italian American mathematician who works in combinatorics, representation theory, and algebraic geometry.

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Affine Hecke algebra

In mathematics, an affine Hecke algebra is the algebra associated to an affine Weyl group, and can be used to prove Macdonald's constant term conjecture for Macdonald polynomials.

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Claudio Procesi

Claudio Procesi (March 31, 1941 in Rome) is an Italian mathematician, known for works in algebra and representation theory.

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In mathematics, a conjecture is a conclusion or proposition based on incomplete information, for which no proof has been found.

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In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

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Hall–Littlewood polynomials

In mathematics, the Hall–Littlewood polynomials are symmetric functions depending on a parameter t and a partition λ.

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Hilbert scheme

In algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space (or a more general projective scheme), refining the Chow variety.

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Ian G. Macdonald

Ian Grant Macdonald (born 11 October 1928 in London, England) is a British mathematician known for his contributions to symmetric functions, special functions, Lie algebra theory and other aspects of algebra, algebraic combinatorics, and combinatorics.

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Jack function

In mathematics, the Jack function is a generalization of the Jack polynomial, introduced by Henry Jack.

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Journal of the American Mathematical Society

The Journal of the American Mathematical Society (JAMS), is a quarterly peer-reviewed mathematical journal published by the American Mathematical Society.

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Kostka polynomial

In mathematics, Kostka polynomials, named after the mathematician Carl Kostka, are families of polynomials that generalize the Kostka numbers.

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Macdonald polynomials

In mathematics, Macdonald polynomials Pλ(x; t,q) are a family of orthogonal symmetric polynomials in several variables, introduced by.

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Mark Haiman

Mark David Haiman is a mathematician at the University of California at Berkeley who proved the Macdonald positivity conjecture for Macdonald polynomials.

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Module (mathematics)

In mathematics, a module is one of the fundamental algebraic structures used in abstract algebra.

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Orthogonal polynomials

In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product.

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Representation theory of the symmetric group

In mathematics, the representation theory of the symmetric group is a particular case of the representation theory of finite groups, for which a concrete and detailed theory can be obtained.

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Root system

In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties.

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Séminaire Lotharingien de Combinatoire

The Séminaire Lotharingien de Combinatoire (Lotharingian Seminar of Combinatorics) is a peer-reviewed academic journal specialising in combinatorial mathematics, named after Lotharingia.

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Schur polynomial

In mathematics, Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the elementary symmetric polynomials and the complete homogeneous symmetric polynomials.

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Stochastic matrix

In mathematics, a stochastic matrix (also termed probability matrix, transition matrix, substitution matrix, or Markov matrix) is a square matrix used to describe the transitions of a Markov chain.

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Symmetric function

In mathematics, a symmetric function of n variables is one whose value given n arguments is the same no matter the order of the arguments.

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Symmetric group

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.

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Zonal spherical function

In mathematics, a zonal spherical function or often just spherical function is a function on a locally compact group G with compact subgroup K (often a maximal compact subgroup) that arises as the matrix coefficient of a K-invariant vector in an irreducible representation of G. The key examples are the matrix coefficients of the spherical principal series, the irreducible representations appearing in the decomposition of the unitary representation of G on L2(G/K).

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[1] https://en.wikipedia.org/wiki/N!_conjecture

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