Symmetric Functions
Schur, Hall–Littlewood, and Macdonald polynomials.
Symmetric Functions. Schur, Hall–Littlewood, and Macdonald polynomials.
Foundations and canonical references
The standard treatments of symmetric functions approach the subject from complementary angles. Macdonald, Symmetric Functions and Hall Polynomials (1995) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Stanley, Enumerative Combinatorics, Volume 2 (1999) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for symmetric functions include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1995Symmetric Functions and Hall Polynomialsmacdonald-1995
- textbook · primary · 1999Enumerative Combinatorics, Volume 2stanley-1999
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