mathematics, Macdonald polynomials Pλ(x; t,q) are a family of orthogonal symmetric polynomials in several variables, introduced by Macdonald in 1987. He...

Legendre polynomials Associated Legendre polynomials Spherical harmonic Lucas polynomials Macdonald polynomials Meixner polynomials Necklace polynomial Newton...

In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to...

sociopathic behavior Macdonald polynomials, in mathematics Old MacDonald Had a Farm, a nursery rhyme Search for "McDonald" , "MacDonald", "Madonald", or "M'Donald"...

elementary symmetric polynomials and the complete homogeneous symmetric polynomials. In representation theory they are the characters of polynomial irreducible...

Kostka polynomials Kλμ(q, t) are known by several names including Kostka–Foulkes polynomials, Macdonald–Kostka polynomials or q,t-Kostka polynomials. Here...

developed a new characterization of both symmetric and nonsymmetric Macdonald polynomials using the combinatorial exclusion process. In 2012, she became one...

mathématiciens (1970, Nice). Vol. 2. pp. 331–335. Macdonald, I. G. (1998). "Constant term polynomials, orthogonal polynomials, and affine Hecke algebras". Doc. Math...

Macdonald conjecture may refer to one of several conjectures: Macdonald's conjectures about Macdonald polynomials Macdonald's generalization of the Dyson...

affine Weyl group, and can be used to prove Macdonald's constant term conjecture for Macdonald polynomials. Let V {\displaystyle V} be a Euclidean space...

theory of Ehrhart polynomials can be seen as a higher-dimensional generalization of Pick's theorem in the Euclidean plane. These polynomials are named after...

polynomials, and is in turn generalized by the Heckman–Opdam polynomials and Macdonald polynomials. The Jack function J κ ( α ) ( x 1 , x 2 , … , x m ) {\displaystyle...

In mathematics, Macdonald-Koornwinder polynomials (also called Koornwinder polynomials) are a family of orthogonal polynomials in several variables, introduced...

a polynomial. In this context other collections of specific symmetric polynomials, such as complete homogeneous, power sum, and Schur polynomials play...

monomial symmetric functions when t is 1 and are special cases of Macdonald polynomials. They were first defined indirectly by Philip Hall using the Hall...

elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed...

other special polynomials, are included. Contents:  Top 0–9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Niels Abel: Abel polynomials - Abelian function...

proved by M. Haiman. It implies Macdonald's positivity conjecture about the Macdonald polynomials. The Macdonald polynomials P λ {\displaystyle P_{\lambda...

Rogers polynomials, also called Rogers–Askey–Ismail polynomials and continuous q-ultraspherical polynomials, are a family of orthogonal polynomials introduced...

common divisors of such polynomials. Gauss's lemma asserts that the product of two primitive polynomials is primitive. (A polynomial with integer coefficients...

developed a new characterization of both symmetric and nonsymmetric Macdonald polynomials using the combinatorial exclusion process. Bergeron, Anne; Corteel...

introduced by Cherednik, who used them to prove Macdonald's constant term conjecture for Macdonald polynomials. Infinitesimal Cherednik algebras have significant...

affine An−1 root system. Macdonald reformulated these conjectures as conjectures about the norms of Macdonald polynomials. Macdonald's conjectures were proved...

the Askey scheme. Askey–Wilson polynomials are the special case of Macdonald polynomials (or Koornwinder polynomials) for the non-reduced affine root...

to expand Macdonald polynomials in terms of LLT polynomials. Ian Grojnowski and Mark Haiman proved a positivity conjecture for LLT polynomials that combined...

power sum symmetric polynomials are a type of basic building block for symmetric polynomials, in the sense that every symmetric polynomial with rational coefficients...

symmetric polynomials in n indeterminates, as n goes to infinity. This ring serves as universal structure in which relations between symmetric polynomials can...

University of California at Berkeley who proved the Macdonald positivity conjecture for Macdonald polynomials. He received his Ph.D in 1984 in the Massachusetts...

homogeneous symmetric polynomials are a specific kind of symmetric polynomials. Every symmetric polynomial can be expressed as a polynomial expression in complete...

elliptic gamma function, elliptic quantum groups, and elliptic Macdonald polynomials). With Alberto Cattaneo in 2000 he gave a path integral interpretation...