## Table of Contents

29 relations: Adriano Garsia, Advances in Mathematics, Affine Hecke algebra, Claudio Procesi, Conjecture, Dimension, Hall–Littlewood polynomials, Hilbert scheme, Ian G. Macdonald, Integer, Jack function, Journal of the American Mathematical Society, Kostka polynomial, Macdonald polynomials, Mark Haiman, Mathematical proof, Mathematics, Module (mathematics), Orthogonal polynomials, Proceedings of the National Academy of Sciences of the United States of America, Representation theory, Representation theory of the symmetric group, Root system, Séminaire Lotharingien de Combinatoire, Schur polynomial, Stochastic matrix, Symmetric function, Symmetric group, Zonal spherical function.

- Algebraic combinatorics
- Theorems about polynomials
- Theorems in linear algebra

## Adriano Garsia

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

See N! conjecture and Adriano Garsia

## Advances in Mathematics

Advances in Mathematics is a peer-reviewed scientific journal covering research on pure mathematics.

See N! conjecture and Advances in Mathematics

## 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. N! conjecture and affine Hecke algebra are representation theory.

See N! conjecture and Affine Hecke algebra

## Claudio Procesi

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

See N! conjecture and Claudio Procesi

## Conjecture

In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof.

See N! conjecture and Conjecture

## Dimension

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.

See N! conjecture and Dimension

## Hall–Littlewood polynomials

In mathematics, the Hall–Littlewood polynomials are symmetric functions depending on a parameter t and a partition λ. N! conjecture and Hall–Littlewood polynomials are algebraic combinatorics and orthogonal polynomials.

See N! conjecture and Hall–Littlewood polynomials

## 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.

See N! conjecture and Hilbert scheme

## Ian G. Macdonald

Ian Grant Macdonald (11 October 1928 – 8 August 2023) was a British mathematician known for his contributions to symmetric functions, special functions, Lie algebra theory and other aspects of algebra, algebraic combinatorics, and combinatorics.

See N! conjecture and Ian G. Macdonald

## Integer

An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.

## Jack function

In mathematics, the Jack function is a generalization of the Jack polynomial, introduced by Henry Jack. N! conjecture and Jack function are orthogonal polynomials.

See N! conjecture and Jack function

## 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.

See N! conjecture and Journal of the American Mathematical Society

## Kostka polynomial

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

See N! conjecture and Kostka polynomial

## Macdonald polynomials

In mathematics, Macdonald polynomials Pλ(x; t,q) are a family of orthogonal symmetric polynomials in several variables, introduced by Macdonald in 1987. N! conjecture and Macdonald polynomials are algebraic combinatorics and orthogonal polynomials.

See N! conjecture and Macdonald polynomials

## Mark Haiman

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

See N! conjecture and Mark Haiman

## Mathematical proof

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion.

See N! conjecture and Mathematical proof

## Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

See N! conjecture and Mathematics

## Module (mathematics)

In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. N! conjecture and module (mathematics) are module theory.

See N! conjecture and Module (mathematics)

## 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.

See N! conjecture and Orthogonal polynomials

## Proceedings of the National Academy of Sciences of the United States of America

Proceedings of the National Academy of Sciences of the United States of America (often abbreviated PNAS or PNAS USA) is a peer-reviewed multidisciplinary scientific journal.

See N! conjecture and Proceedings of the National Academy of Sciences of the United States of America

## Representation theory

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.

See N! conjecture and Representation theory

## 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.

See N! conjecture and Representation theory of the symmetric group

## Root system

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

See N! conjecture and Root system

## Séminaire Lotharingien de Combinatoire

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

See N! conjecture and Séminaire Lotharingien de Combinatoire

## 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. N! conjecture and Schur polynomial are orthogonal polynomials.

See N! conjecture and Schur polynomial

## Stochastic matrix

In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain.

See N! conjecture and Stochastic matrix

## Symmetric function

In mathematics, a function of n variables is symmetric if its value is the same no matter the order of its arguments.

See N! conjecture and Symmetric function

## 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.

See N! conjecture and Symmetric group

## 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).

See N! conjecture and Zonal spherical function

## See also

### Algebraic combinatorics

- Algebraic combinatorics
- Antimatroid
- Association scheme
- Bender–Knuth involution
- Bose–Mesner algebra
- Buekenhout geometry
- Building (mathematics)
- Cameron–Fon-Der-Flaass IBIS theorem
- Coherent algebra
- Combinatorial commutative algebra
- Combinatorial species
- Combinatorics: The Rota Way
- Coxeter complex
- Differential poset
- Dominance order
- Dyson conjecture
- Eulerian poset
- Finite ring
- Gamas's theorem
- Garnir relations
- Graded poset
- H-vector
- Hall–Littlewood polynomials
- Hessenberg variety
- Incidence algebra
- Jeu de taquin
- Kazhdan–Lusztig polynomial
- Kronecker coefficient
- Kruskal–Katona theorem
- LLT polynomial
- Lattice word
- Littelmann path model
- Littlewood–Richardson rule
- Macdonald polynomials
- N! conjecture
- Newton's identities
- Picture (mathematics)
- Quasi-polynomial
- Quasisymmetric function
- Restricted representation
- Ring of symmetric functions
- Robinson–Schensted correspondence
- Robinson–Schensted–Knuth correspondence
- Schubert polynomial
- Schubert variety
- Simplicial sphere
- Stanley's reciprocity theorem
- Stanley–Reisner ring
- Viennot's geometric construction

### Theorems about polynomials

- Abel–Ruffini theorem
- Bernstein's theorem (polynomials)
- Binomial theorem
- Cohn's theorem
- Complex conjugate root theorem
- Descartes' rule of signs
- Eilenberg–Niven theorem
- Equioscillation theorem
- Factor theorem
- Fundamental theorem of algebra
- Gauss's lemma (polynomials)
- Gauss–Lucas theorem
- Grace–Walsh–SzegÅ‘ theorem
- Hilbert's basis theorem
- Hilbert's irreducibility theorem
- Kharitonov's theorem
- Lagrange's theorem (number theory)
- Marden's theorem
- Mason–Stothers theorem
- Multi-homogeneous Bézout theorem
- Multinomial theorem
- N! conjecture
- Polynomial remainder theorem
- Rational root theorem
- Routh–Hurwitz theorem
- Schwartz–Zippel lemma
- Sturm's theorem

### Theorems in linear algebra

- Cayley–Hamilton theorem
- Chebotarev theorem on roots of unity
- Cramer's rule
- Dimension theorem for vector spaces
- Gerbaldi's theorem
- Goddard–Thorn theorem
- Hawkins–Simon condition
- MacMahon's master theorem
- N! conjecture
- Perron–Frobenius theorem
- Principal axis theorem
- Rank–nullity theorem
- Rouché–Capelli theorem
- Schur's theorem
- Schur–Horn theorem
- Sinkhorn's theorem
- Specht's theorem
- Spectral theorem
- Stein-Rosenberg theorem
- Sylvester's determinant identity
- Sylvester's law of inertia
- Weinstein–Aronszajn identity
- Witt's theorem

## References

Also known as N factorial conjecture, N!-conjecture.