What does macdonald polynomial mean?
Definitions for macdonald polynomial
mac·don·ald po·ly·no·mi·al
This dictionary definitions page includes all the possible meanings, example usage and translations of the word macdonald polynomial.
Wiktionary
Macdonald polynomialnoun
Any of a two-parameter family of orthogonal polynomials indexed by a positive weight of a root system.
Etymology: Introduced by Ian G. Macdonald in 1987.
Wikipedia
macdonald polynomial
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.
Numerology
Chaldean Numerology
The numerical value of macdonald polynomial in Chaldean Numerology is: 9
Pythagorean Numerology
The numerical value of macdonald polynomial in Pythagorean Numerology is: 1
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"macdonald polynomial." Definitions.net. STANDS4 LLC, 2024. Web. 25 Apr. 2024. <https://www.definitions.net/definition/macdonald+polynomial>.
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