Reference
Generated from the usage messages of each package. Each page links to the corresponding background pages on symmetricfunctions.com.
| Package | Contents |
|---|---|
| SymmetricFunctions | Monomial, elementary, complete homogeneous, power-sum, Schur and forgotten bases with fast transition matrices; several alphabets; Hall and Jack inner products; plethysm; Kostka, inverse Kostka, Littlewood–Richardson and Kronecker coefficients; skew Schur, Schur P and Q, Jack, Hall–Littlewood, Macdonald P/J and modified Macdonald H~ (Haglund’s convention), LLT, k-Schur, Lah and Petrie functions; the Delta and nabla operators |
| ShiftedSymmetricFunctions | Okounkov–Olshanski shifted Schur and Jack polynomials, normalized characters, and Stanley–Feray–Sniady multirectangular character polynomials |
| CombinatoricTools | Partitions, compositions, set partitions, permutation statistics, q-analogs, characters of the symmetric group, Kostka numbers |
| NewTableaux | Standard and semistandard (skew) Young tableaux, RSK, promotion, evacuation, crystal operators, border strips, TeX output; semistandard augmented fillings (SSAF) with statistics, crystals and Mason insertion |
| GTPatterns | Gelfand–Tsetlin patterns (skew, row-flagged, cylindric), BZ patterns, Gog and Magog patterns, tiles and snakes, lattice paths, stretched Kostka (Ehrhart) data, TikZ output |
| QuasiSymmetricFunctions | Monomial, fundamental and power-sum quasisymmetric functions, quasisymmetric Schur functions, and bridges to polynomials and to symmetric functions |
| PolynomialTools | Real-rootedness, interlacing, log-concavity, Eulerian and h*-polynomials, recurrence finding, Hilbert functions |
| PermutationTools | Pattern avoidance, Foata and related maps, Bruhat and weak order, families of permutations |
| CatalanObjects | Dyck paths, non-crossing partitions and matchings, parking functions, trees and other Catalan families, with plots |
| UnicellularChromatics | Chromatic symmetric functions and LLT polynomials of unit interval graphs and area sequences, orientations and their statistics |
| GraphTools | Graph polynomials, orientations, and datasets of connected graphs (n <= 9), trees (n <= 20) and rooted trees (n <= 10) |
| MatroidTools | Matroids from bases: rank, duality, deletion/contraction, Tutte polynomials, transversal, lattice path and rook matroids |
| NonsymmetricPolynomials | Divided difference, Demazure and Demazure–Lusztig operators (also K-theoretic); key, atom, t-key, t-atom, Schubert, Grothendieck, Lascoux, fundamental slide, lock and dual Grothendieck polynomials; nonsymmetric Macdonald polynomials (also with permuted basements) and nonsymmetric Jack polynomials; basis symbols with conversions |
| LegacyConversions | Converters from the data of the legacy packages (GT patterns, tableaux, area lists, key indices) to the supported conventions |