Abstract
Abstract This is a new and much expanded edition of Professor Macdonald's acclaimed monograph on Symmetric Functions and Hall Polynomials. Almost every chapter has new sections and many new examples have been included throughout. In addition there are two new chapters (6 and 7). Chapter 6 contains an extended account of a family of symmetric functions depending on two parameters. These symmetric functions include as particular cases many of those encountered earlier in the book and they also include, as a limiting case, Jack's symmetric functions depending on a parameter a. Many of the properties of the Schur functions generalize to these two-parameter symmetric functions. Chapter 7 is devoted to the study of the zxonal polynomials, long familiar to staticians. From one point of view, they are a special case of Jack's symmetric functions (the parameter a being equal to 2) but their combinatorial and group-theoretic connections make them worthy of study in their own right.
Keywords
Symmetric functionStanley symmetric functionComplete homogeneous symmetric polynomialSchur polynomialRing of symmetric functionsSymmetric groupMathematicsElementary symmetric polynomialPure mathematicsSymmetric polynomialLimitingPower sum symmetric polynomialOrthogonal polynomialsCombinatoricsAlgebra over a fieldMacdonald polynomialsMathematical analysisPolynomialClassical orthogonal polynomials
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Publication Info
- Year
- 1995
- Type
- book
- Citations
- 7630
- Access
- Closed
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Cite This
I. G. Macdonald
(1995).
Symmetric Functions and Hall Polynomials.
.
https://doi.org/10.1093/oso/9780198534891.001.0001
Identifiers
- DOI
- 10.1093/oso/9780198534891.001.0001