2022-12-30
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 fixed-point free Stanley symmetric functionsSym 2019 1 Schubert
Affine involution Stanley symmetric functionsSym 2018 1 Schubert
Affine Schubert polynomialsAll 2006 1
Affine Schur functionsSym 2006 2 Schur
Affine Stanley symmetric functionsSym 2006 2 Schubert
Big Schur functionsSym 2017 1
Boolean product polynomialsSym 2018 1 Other
Bottom Schur functionsSym 2004 2 Schur
Canonical stable Grothendieck polynomialsSym 2017 2 Schubert
Catalan symmetric functionsSym 2010 4 Schur
Character symmetric functionsSym 2016 1 Schur
Chromatic quasisymmetric functionsSym 2012 7
Colored Eulerian quasisymmetric functionsSym 2012 1 Other
Complete homogeneous symmetric functionsSym 1700 5
Cycle index polynomialsSym 1937 2 Other
Cylindric complete homogeneous polynomialsCSym 2005 1 Elementary
Cylindric elementary polynomialsCSym 2005 1 Elementary
Cylindric Schur polynomialsSym 2005 5
Demazure atomsAll 1990 4 Schur
Double Grothendieck polynomialsAll 1994 1 Schubert
Double Schubert polynomialsAll 1982 1 Schubert
Double Stanley symmetric functionsSym 2018 1 Schubert
Dual immaculate Schur functionsQSym 2014 1 Schur
Dual stable Grothendieck polynomialsSym 2007 2 Schur
Elementary symmetric functionsSym 1700 5
Eulerian quasisymmetric functionsSym 2010 3 Other
Extended chromatic symmetric functionsSym 2019 2
Extended Schur functionsQSym 2019 1 Schur
Factorial supersymmetric Schur polynomialsSuperSym 1996 1 Schur
Flagged factorial Grothendieck polynomialsAll 2019 1 Schubert
Forgotten symmetric functionsSym 1900 3
Fundamental slide polynomialsAll 2016 1 Schur
Generalized and refined dual stable Grothendieck polynomialsSym 2016 1 Schur
Generalized Demazure atomsAll 2012 1 Schur
Gessel quasisymmetric functionsQSym 1984 4 QuasiElementary
Grassman Grothendieck polynomialsSym 1994 5 Schubert
Grothendieck polynomialsAll 1990 2 Schubert
Hall–Littlewood PSym 1961 5 Schur
Hall–Littlewood QSym 1961 4 Schur
Hivert polynomialsQSym 2000 1 Schur
Hook Schur polynomialsSuperSym 1983 5 Schur
Interpolation Macdonald P polynomialsShiftedSym 1998 2 Schur
Involution Schubert polynomialsAll 2018 1
Involution Stanley symmetric functionsSym 2017 1 Schubert
Jack interpolation polynomialsAll 1994 2 Schur
Jack J polynomialsSym 1970 5 Schur
Jack P polynomialsSym 1970 5 Schur
Katalan symmetric functionsSym 2020 1 Schur
Key polynomialsAll 1974 5 Schur
Kohnert polynomialsAll 2019 1 Schur
K-theoretic Schur P/Q polynomialsSym 2013 1 Schur
Lah symmetric functionsSym 2019 1 Other
Lascoux atomAll 2004 2 Schur
Lascoux polynomialsAll 2004 2 Schur
Lecture hall Schur functionsAll 2018 1 Schur
LLT polynomialsSym 1997 5 Schur
Lock polynomialsAll 2019 1 Schur
Loop Schur polynomialsLSym 2012 4 Schur
Lyndon symmetric functionsSym 1993 2 Sym
Macdonald E polynomialsAll 1995 2 Schur
Macdonald J polynomialsSym 1987 4 Schur
Macdonald P polynomialsSym 1987 4 Schur
Modified Hall–Littlewood polynomialsSym 1961 5 Schur
Modified Macdonald polynomialsSym 1987 5 Schur
Modular Schur functionsSym 1992 1 Schur
Monomial quasisymmetric functionsQSym 1984 5 QuasiElementary
Monomial slide polynomialsAll 2016 1 Schur
Monomial symmetric functionsSym 1700 5
Multi-Macdonald P polynomialsOther 2019 1 Schur
Non-commutative Schur functionsNSym 1995 1 Schur
Non-commutative unicellular LLT polynomialsWQSym 2019 1 Other
Non-symmetric q-Whittaker polynomialsAll 1995 2 Schur
Odd Schur functionsOSym 2012 1 Schur
Orthogonal Schur polynomialsOther 1971? 1 Schur
Peak quasisymmetric functionsPQSym 1997 2 Quasi
Permuted basement Macdonald E polynomialsAll 2011 1 Schur
Petrie symmetric functionsSym 1992 1 Other
P-Grothendieck polynomialsSym 2020 1 Schur
Powersum quasisymmetric functions (p)QSym 2021 2 QuasiElementary
Powersum quasisymmetric functions (Phi)QSym 2017 3 QuasiElementary
Powersum quasisymmetric functions (Psi)QSym 2017 3 QuasiElementary
Powersum symmetric functionsSym 1700 5
P-partitionsQSym 1984 1 QuasiElementary
Quantum double Grothendieck polynomialsAll 2006 1 Schubert
Quantum Double Schubert polynomialsAll 2000 1
Quantum Schubert polynomialsAll 1997 3
Quasisymmetric Macdonald E polynomialsQSym 2019 1 Schur
Quasisymmetric Macdonald J polynomialsQSym 2022 1 Schur
Quasisymmetric Schur functionsQSym 2011 1 Schur
q-Whittaker polynomialsAll 1995 2 Schur
Restricted Schur polynomialsOther 2007 1
Ribbon Schur polynomialsSym 1901 5 Schur
Row-strict dual immaculate Schur functionsQSym 2022 1 Schur
Row-strict quasisymmetric Schur functionsQSym 2013 1 Schur
Row-strict Young quasisymmetric Schur functionsQSym 2013 1 Schur
Schubert polynomialsAll 1982 5
Schur functions in non-commuting variablesNCSym 1995 2 2022
Schur multiple zeta functionsNA 2018 1 Schur
Schur polynomialsSym 1841 8
Schur polynomials (flagged)All 1982 2 Schur
Schur-S polynomialsAll ? 1 Schur
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 affine Schur functionsSym 2006 2 Schur
Skew Schubert polynomialsAll 2003 1
Skew Schur polynomialsSym 1901 5 Schur
Stable Grothendieck polynomialsSym 1994 2 Schubert
Stanley symmetric functionsSym 1984 5 Schubert
Symplectic Schur polynomialsOther 1971? 1 Schur
Symplectic $Q$ functionsOther 2020 1 Schur
Toric Schur polynomialsSym 2005 5
Transformed Hall–LittlewoodSym 1961 5 Schur
Tutte symmetric functionsSym 1998 1
Twisted Schubert polynomialsAll 2019 1
Type B/C/D Schubert polynomialsAll 1996 2 Schubert
Type B/C Stanley symmetric functionsSym 1996 2 Schubert
Type $B/C$ Demazure atomsAll 2009 1 Schur
Type $B/C$ key polynomialsAll 2009 1 Schur
Unicellular LLT polynomialsSym 2005 4 Schur
Universal Schubert polynomialsAll 1999 1
Whittaker functionsSym 1967 1 Schur
Wreath Macdonald P polynomialsOther 2002 1 Schur
Wreath product Schur polynomialsOther 2009 1 Schur
Young quasisymmetric Schur functionsQSym 2013 1 Schur
Zonal symmetric functionsSym 1963 3 Schur
$k$-Schur polynomialsSym* 2003 4 Schur