The symmetric functions catalog

An overview of symmetric functions and related topics

2019-05-21

Index of polynomials

Below is the list of all families of symmetric functions and related families of polynomials currently covered.

Next to each link is the vector space where they live, year when they were introduced, and my personal judgement of how much information I have managed to write down about the family.

Affine Schur functionsSym 2006 2 Schur
Bottom Schur functionsSym 2004 2 Schur
Cycle index polynomialsSym 1937 2 Other
Cylindric elementary polynomialsCSym 2005 1 Elementary
Demazure atomsAll 1990 4 Schur
Double Schubert polynomialsAll 1982 1 Schubert
Gessel quasisymmetric functionsQSym 1984 4 QuasiElementary
Grothendieck polynomialsAll 1990 2 Schubert
Hall–Littlewood PSym 1961 5 Schur
Hall–Littlewood QSym 1961 4 Schur
Hook Schur polynomialsSuperSym 1983 5 Schur
Jack J polynomialsSym 1970 5 Schur
Jack P polynomialsSym 1970 5 Schur
Key polynomialsAll 1974 5 Schur
LLT polynomialsSym 1997 5 Schur
Loop Schur polynomialsLSym 2012 4 Schur
Macdonald E polynomialsAll 1995 1 Schur
Macdonald J polynomialsSym 1987 4 Schur
Macdonald P polynomialsSym 1987 4 Schur
Monomial quasisymmetric functionsQSym 1984 5 QuasiElementary
Orthogonal Schur polynomialsOther 1971? 1 Schur
Powersum quasisymmetric functions (Phi)QSym 2017 3 QuasiElementary
Powersum quasisymmetric functions (Psi)QSym 2017 3 QuasiElementary
P-partitionsQSym 1984 1 QuasiElementary
Schur's $P$ functionsSym 1911 4 Schur
Schur's $Q$ functionsSym 1911 3 Schur
Shifted Jack polynomialsShiftedSym 1994 3 Schur
Shifted Schur polynomialsShiftedSym 1996 3
Skew Schur polynomialsSym 1901 5 Schur
Stanley symmetric functionsSym 1984 5 Schubert
Symplectic Schur polynomialsOther 1971? 1 Schur
Type $B/C$ Demazure atomsAll 2009 1 Schur
Zonal symmetric functionsSym 1963 3 Schur
$k$-Schur polynomialsSym* 2003 4 Schur