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Index and list of polynomials
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Index and list of polynomials
Maintained by Per Alexandersson,
[email protected].
The symmetric functions catalog
An overview of symmetric functions and related topics
Index CSP Topics Meta2021-03-04
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 Schubert polynomialsAll 2006 1
Affine Schur functionsSym 2006 2
Affine Stanley symmetric functionsSym 2006 2
Boolean product polynomialsSym 2018 1
Bottom Schur functionsSym 2004 2
Catalan symmetric functionsSym 2010 4
Character symmetric functionsSym 2016 1
Chromatic quasisymmetric functionsSym 2012 7
Complete homogeneous symmetric functionsSym 1700 5
Cycle index polynomialsSym 1937 2
Cylindric complete homogeneous polynomialsCSym 2005 1
Cylindric elementary polynomialsCSym 2005 1
Cylindric Schur polynomialsSym 2005 5
Demazure atomsAll 1990 4
Double Grothendieck polynomialsAll 1994 1
Double Schubert polynomialsAll 1982 1
Double Stanley symmetric functionsSym 2018 1
Dual stable Grothendieck polynomialsSym 2007 2
Elementary symmetric functionsSym 1700 5
Eulerian quasisymmetric functionsSym 2010 3
Extended chromatic symmetric functionsSym 2019 2
Factorial supersymmetric Schur polynomialsSuperSym 1996 1
Forgotten symmetric functionsSym 1900 3
Generalized Demazure atomsAll 2012 1
Gessel quasisymmetric functionsQSym 1984 4
Grassman Grothendieck polynomialsSym 1994 5
Grothendieck polynomialsAll 1990 2
Hall–Littlewood PSym 1961 5
Hall–Littlewood QSym 1961 4
Hivert polynomialsQSym 2000 1
Hook Schur polynomialsSuperSym 1983 5
Interpolation Macdonald P polynomialsShiftedSym 1998 2
Involution Schubert polynomialsAll 2018 1
Involution Stanley symmetric functionsSym 2017 1
Jack interpolation polynomialsAll 1994 2
Jack J polynomialsSym 1970 5
Jack P polynomialsSym 1970 5
Katalan symmetric functionsSym 2020 1
Key polynomialsAll 1974 5
K-theoretic Schur P/Q polynomialsSym 2013 1
Lah symmetric functionsSym 2019 1
Lecture hall Schur functionsAll 2018 1
LLT polynomialsSym 1997 5
Loop Schur polynomialsLSym 2012 4
Macdonald E polynomialsAll 1995 2
Macdonald J polynomialsSym 1987 4
Macdonald P polynomialsSym 1987 4
Modified Hall–Littlewood polynomialsSym 1961 5
Modified Macdonald polynomialsSym 1987 5
Modular Schur functionsSym 1992 1
Monomial quasisymmetric functionsQSym 1984 5
Monomial symmetric functionsSym 1700 5
Multi-Macdonald P polynomialsOther 2019 1
Non-commutative Schur functionsNCSym 1995 1
Non-commutative unicellular LLT polynomialsWQSym 2019 1
Non-symmetric q-Whittaker polynomialsAll 1995 2
Odd Schur functionsOSym 2012 1
Orthogonal Schur polynomialsOther 1971? 1
Peak quasisymmetric functionsPQSym 1997 2
Petrie symmetric functionsSym 1992 1
P-Grothendieck polynomialsSym 2020 1
Powersum quasisymmetric functions (Phi)QSym 2017 3
Powersum quasisymmetric functions (Psi)QSym 2017 3
Powersum symmetric functionsSym 1700 5
P-partitionsQSym 1984 1
Quantum double Grothendieck polynomialsAll 2006 1
Quantum Double Schubert polynomialsAll 2000 1
Quantum Schubert polynomialsAll 1997 3
Quasisymmetric Macdonald E polynomialsQSym 2019 1
q-Whittaker polynomialsAll 1995 2
Restricted Schur polynomialsOther 2007 1
Ribbon Schur polynomialsSym 1901 5
Schubert polynomialsAll 1982 5
Schur polynomialsSym 1841 8
Schur polynomials (flagged)All 1982 2
Schur-S polynomialsAll ? 1
Schur's P functionsSym 1911 4
Schur's Q functionsSym 1911 3
Shifted Jack polynomialsShiftedSym 1994 3
Shifted Schur polynomialsShiftedSym 1996 3
Skew affine Schur functionsSym 2006 2
Skew Schubert polynomialsAll 2003 1
Skew Schur polynomialsSym 1901 5
Stable Grothendieck polynomialsSym 1994 2
Stanley symmetric functionsSym 1984 5
Symplectic Schur polynomialsOther 1971? 1
Symplectic Q functionsOther 2020 1
Toric Schur polynomialsSym 2005 5
Transformed Hall–LittlewoodSym 1961 5
Tutte symmetric functionsSym 1998 1
Twisted Schubert polynomialsAll 2019 1
Type B/C/D Schubert polynomialsAll 1996 2
Type B/C Stanley symmetric functionsSym 1996 2
Type B/C Demazure atomsAll 2009 1
Type B/C key polynomialsAll 2009 1
Unicellular LLT polynomialsSym 2005 4
Universal Schubert polynomialsAll 1999 1
Whittaker functionsSym 1967 1
Wreath product Schur polynomialsOther 2009 1
Zonal symmetric functionsSym 1963 3
k-Schur polynomialsSym* 2003 4
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