Definitions for macdonald polynomials
mac·don·ald po·ly·no·mi·als

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1. 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. He later introduced a non-symmetric generalization in 1995. Macdonald originally associated his polynomials with weights λ of finite root systems and used just one variable t, but later realized that it is more natural to associate them with affine root systems rather than finite root systems, in which case the variable t can be replaced by several different variables t=(t1,...,tk), one for each of the k orbits of roots in the affine root system. The Macdonald polynomials are polynomials in n variables x=(x1,...,xn), where n is the rank of the affine root system. They generalize many other families of orthogonal polynomials, such as Jack polynomials and Hall–Littlewood polynomials and Askey–Wilson polynomials, which in turn include most of the named 1-variable orthogonal polynomials as special cases. Koornwinder polynomials are Macdonald polynomials of certain non-reduced root systems. They have deep relationships with affine Hecke algebras and Hilbert schemes, which were used to prove several conjectures made by Macdonald about them.

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1. Macdonald polynomials

   In mathematics, Macdonald polynomials Pλ are a family of orthogonal polynomials in several variables, introduced by Macdonald . Macdonald originally associated his polynomials with weights λ of finite root systems and used just one variable t, but later realized that it is more natural to associate them with affine root systems rather than finite root systems, in which case the variable t can be replaced by several different variables t=, one for each of the k orbits of roots in the affine root system. The Macdonald polynomials are polynomials in n variables x=, where n is the rank of the affine root system. They generalize many other families of orthogonal polynomials, such as Jack polynomials and Hall–Littlewood polynomials and Askey–Wilson polynomials, which in turn include most of the named 1-variable orthogonal polynomials as special cases. Koornwinder polynomials are Macdonald polynomials of certain non-reduced root systems. They have deep relationships with affine Hecke algebras and Hilbert schemes, which were used to prove several conjectures made by Macdonald about them.

How to pronounce macdonald polynomials?

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Numerology

1. Chaldean Numerology

   The numerical value of macdonald polynomials in Chaldean Numerology is: 3

2. Pythagorean Numerology

   The numerical value of macdonald polynomials in Pythagorean Numerology is: 2

References

1. ^ Wikipedia
   https://en.wikipedia.org/wiki/Macdonald_Polynomials
2. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=macdonald polynomials