Comprehensive Module list¶
Note
This list is currently sorted in alphabetical order w.r.t. the module names.
It can be updated semi-automatically by running in src/sage/combinat:
find -name "*.py*" | sed 's|\.pyx\?$||; s|\./| sage/combinat/|' | LANG=en_US.UTF-8 LC_COLLATE=C sort > /tmp/module_list.rst
and copy pasting the result back there.
Todo
See trac ticket #17421 for desirable improvements.
- Combinatorics
- Abstract Recursive Trees
- Affine Permutations
- Algebraic combinatorics
- Combinatorics features that are imported by default in the interpreter namespace
- Alternating Sign Matrices
- Backtracking
- Baxter permutations
- Binary Recurrence Sequences.
- Binary Trees
- Cartesian Products
- Enumerated sets of partitions, tableaux, …
- Combinatorial Hopf algebras
- Poirier-Reutenauer Hopf algebra of standard tableaux
- Word Quasi-symmetric functions
- Cluster Algebras and Quivers
- Cluster algebra and quivers features that are imported by default in the interpreter namespace
- ClusterSeed
- mutation_class
- This file contains helper functions for detecting the mutation type of
- Quiver
- Quiver mutation types
- Cluster complex (or generalized dual associahedron)
- Colored Permutations
- Combinatorial Functions
- Fast computation of combinatorial functions (Cython + mpz).
- Combinations
- Combinatorial Algebras
- Combinatorial maps
- Integer compositions
- Signed Compositions
- Composition Tableaux
- Constellations
- Cores
- Counting
- Crystals
- Affine Crystals
- Affine factorization crystal of type \(A\)
- Affinization Crystals
- Alcove paths
- Crystal features that are imported by default in the interpreter namespace
- Benkart-Kang-Kashiwara crystals for the general-linear Lie superalgebra
- Catalog Of Crystals
- Catalog Of Elementary Crystals
- Catalog Of Crystal Models For \(B(\infty)\)
- Catalog Of Crystal Models For Kirillov-Reshetikhin Crystals
- An introduction to crystals
- Direct Sum of Crystals
- Elementary Crystals
- Fast Rank Two Crystals
- Crystals of Generalized Young Walls
- Highest weight crystals
- Induced Crystals
- \(\mathcal{B}(\infty)\) Crystals of Tableaux in Nonexceptional Types and \(G_2\)
- Crystals of Kac modules of the general-linear Lie superalgebra
- Kirillov-Reshetikhin Crystals
- Kyoto Path Model for Affine Highest Weight Crystals
- Crystals of letters
- Littelmann paths
- Crystals of Modified Nakajima Monomials
- Crystal of Bernstein-Zelevinsky Multisegments
- Crystal Of Mirković-Vilonen (MV) Polytopes
- \(\mathcal{B}(\infty)\) Crystal Of PBW Monomials.
- PBW Data
- Polyhedral Realization of \(B(\infty)\)
- Spin Crystals
- Star-Crystal Structure On \(B(\infty)\)
- Tensor Products of Crystals
- Tensor Products of Crystal Elements
- Cyclic sieving phenomenon
- De Bruijn sequences
- Degree sequences
- Derangements
- Descent Algebras
- Combinatorial Designs and Incidence Structures
- Combinatorial design features that are imported by default in the interpreter namespace
- Balanced Incomplete Block Designs (BIBD)
- Resolvable Balanced Incomplete Block Design (RBIBD)
- Group-Divisible Designs (GDD)
- Block designs
- Covering designs: coverings of \(t\)-element subsets of a \(v\)-set by \(k\)-sets
- Database of small combinatorial designs
- Catalog of designs
- Cython functions for combinatorial designs
- Difference families
- Difference Matrices
- Evenly distributed sets in finite fields
- External Representations of Block Designs
- Incidence structures (i.e. hypergraphs, i.e. set systems)
- Mutually Orthogonal Latin Squares (MOLS)
- Orthogonal arrays (OA)
- Orthogonal arrays (build recursive constructions)
- Orthogonal arrays (find recursive constructions)
- Steiner Quadruple Systems
- Hypergraph isomorphic copy search
- Two-graphs
- Diagram and Partition Algebras
- Exact Cover Problem via Dancing Links
- Dyck Words
- Substitutions over unit cube faces (Rauzy fractals)
- Enumerated sets and combinatorial objects
- Tools for enumeration modulo the action of a permutation group
- Compute Bell and Uppuluri-Carpenter numbers
- Families
- Finite State Machines, Automata, Transducers
- Common Automata and Transducers (Finite State Machines Generators)
- Free Quasi-symmetric functions
- Free modules
- Free Dendriform Algebras
- Free Pre-Lie Algebras
- Fully packed loops
- Gelfand-Tsetlin Patterns
- Paths in Directed Acyclic Graphs
- Gray codes
- Growth diagrams and dual graded graphs
- Grossman-Larson Hopf Algebras
- Hall Polynomials
- The Hillman-Grassl correspondence
- Enumerated set of lists of integers with constraints: base classes
- Enumerated set of lists of integers with constraints: front-end
- Enumerated set of lists of integers with constraints, in inverse lexicographic order
- Counting, generating, and manipulating non-negative integer matrices
- (Non-negative) Integer vectors
- Weighted Integer Vectors
- Integer vectors modulo the action of a permutation group
- Tamari Interval-posets
- Strong and weak tableaux
- Kazhdan-Lusztig Polynomials
- Knutson-Tao Puzzles
- Combinatorics on matrices
- Combinatorics on matrix features that are imported by default in the interpreter namespace
- Dancing Links internal pyx code
- Dancing links C++ wrapper
- Hadamard matrices
- Latin Squares
- Miscellaneous
- Ordered Multiset Partitions into Sets and the Minimaj Crystal
- Non-Commutative Symmetric Functions and Quasi-Symmetric Functions
- Features that are imported by default in the interpreter namespace
- Common combinatorial tools
- Generic code for bases
- Non-Commutative Symmetric Functions
- Quasisymmetric functions
- Introduction to Quasisymmetric Functions
- Symmetric Functions in Non-Commuting Variables
- Features that are imported by default in the interpreter namespace
- Bases for \(NCSym\).
- Dual Symmetric Functions in Non-Commuting Variables
- Symmetric Functions in Non-Commuting Variables
- Necklaces
- Non-Decreasing Parking Functions
- Ordered Rooted Trees
- Output functions
- Parallelogram Polyominoes
- Parking Functions
- Plane Partitions
- Integer partitions
- Partition/Diagram Algebras
- Kleshchev partitions
- Partition tuples
- Number of partitions of an integer
- Perfect matchings
- Permutations
- Permutations (Cython file)
- Posets
- Poset features that are imported by default in the interpreter namespace
- Cartesian products of Posets
- Elements of posets, lattices, semilattices, etc.
- Hasse diagrams of posets
- Incidence Algebras
- Finite lattices and semilattices
- Linear Extensions of Posets
- Möbius Algebras
- A catalog of posets and lattices.
- Finite posets
- \(q\)-Analogues
- \(q\)-Bernoulli Numbers and Polynomials
- Combinatorics quickref
- Rankers
- Restricted growth arrays
- Ribbons
- Ribbon Shaped Tableaux
- Ribbon Tableaux
- Rigged Configurations
- Features that are imported by default in the interpreter namespace
- Abstract classes for the rigged configuration bijections
- Bijection between rigged configurations for \(B(\infty)\) and marginally large tableaux
- Bijection classes for type \(A_n^{(1)}\)
- Bijection classes for type \(A_{2n}^{(2)\dagger}\).
- Bijection classes for type \(A_{2n}^{(2)}\).
- Bijection classes for type \(A_{2n-1}^{(2)}\).
- Bijection classes for type \(B_n^{(1)}\).
- Bijection classes for type \(C_n^{(1)}\).
- Bijection classes for type \(D_n^{(1)}\)
- Bijection classes for type \(D_{n+1}^{(2)}\).
- Bijection classes for type \(D_4^{(3)}\).
- Bijection between rigged configurations and KR tableaux
- Kleber Trees
- Kirillov-Reshetikhin Tableaux
- Crystal of Rigged Configurations
- Rigged Configurations of \(\mathcal{B}(\infty)\)
- Rigged Configuration Elements
- Rigged Configurations
- Rigged Partitions
- Tensor Product of Kirillov-Reshetikhin Tableaux
- Tensor Product of Kirillov-Reshetikhin Tableaux Elements
- Root Systems
- Root system features that are imported by default in the interpreter namespace
- Ambient lattices and ambient spaces
- Associahedron
- Braid Move Calculator
- Braid Orbit
- Branching Rules
- Cartan matrices
- Cartan types
- Coxeter Groups
- Coxeter Matrices
- Coxeter Types
- Dynkin diagrams
- Hecke algebra representations
- Integrable Representations of Affine Lie Algebras
- Nonsymmetric Macdonald polynomials
- Pieri Factors
- Tutorial: visualizing root systems
- Finite complex reflection groups
- Finite real reflection groups
- Group algebras of root lattice realizations
- Root lattice realizations
- Root lattices and root spaces
- Root systems
- Root system data for super type A
- Root system data for type A
- Root system data for (untwisted) type A affine
- Root system data for type A infinity
- Root system data for type B
- Root system data for type BC affine
- Root system data for (untwisted) type B affine
- Root system data for type C
- Root system data for (untwisted) type C affine
- Root system data for type D
- Root system data for (untwisted) type D affine
- Root system data for type E
- Root system data for (untwisted) type E affine
- Root system data for type F
- Root system data for (untwisted) type F affine
- Root system data for type G
- Root system data for (untwisted) type G affine
- Root system data for type H
- Root system data for type I
- Root system data for type Q
- Root system data for affine Cartan types
- Root system data for dual Cartan types
- Extended Affine Weyl Groups
- Fundamental Group of an Extended Affine Weyl Group
- Root system data for folded Cartan types
- Root system data for Cartan types with marked nodes
- Root system data for reducible Cartan types
- Root system data for relabelled Cartan types
- Weight lattice realizations
- Weight lattices and weight spaces
- Weyl Character Rings
- Weyl Groups
- Rooted (Unordered) Trees
- Robinson-Schensted-Knuth correspondence
- Schubert Polynomials
- Set Partitions
- Ordered Set Partitions
- Symmetric Functions
- Symmetric function features that are imported by default in the interpreter namespace
- Characters of the symmetric group as bases of the symmetric functions
- Classical symmetric functions.
- Generic dual bases symmetric functions
- Elementary symmetric functions
- Hall-Littlewood Polynomials
- Hecke Character Basis
- Homogeneous symmetric functions
- Jack Symmetric Functions
- Quotient of symmetric function space by ideal generated by Hall-Littlewood symmetric functions
- Kostka-Foulkes Polynomials
- LLT symmetric functions
- Macdonald Polynomials
- Monomial symmetric functions
- Multiplicative symmetric functions
- \(k\)-Schur Functions
- Non-symmetric Macdonald Polynomials
- Orthogonal Symmetric Functions
- Symmetric functions defined by orthogonality and triangularity.
- Power sum symmetric functions
- Schur symmetric functions
- Symplectic Symmetric Functions
- Symmetric functions, with their multiple realizations
- Symmetric Functions
- Witt symmetric functions
- Shard intersection order
- Shifted primed tableaux
- Shuffle product of iterables
- Sidon sets and their generalizations, Sidon \(g\)-sets
- Similarity class types of matrices with entries in a finite field
- sine-Gordon Y-system plotter
- Six Vertex Model
- Skew Partitions
- Skew Tableaux
- Functions that compute some of the sequences in Sloane’s tables
- Combinatorial Species
- Combinatorial species features that are imported by default in the interpreter namespace
- Characteristic Species
- Composition species
- Cycle Species
- Empty Species
- Functorial composition species
- Generating Series
- Examples of Combinatorial Species
- Linear-order Species
- Miscellaneous Functions
- Partition Species
- Permutation species
- Sum species
- Recursive Species
- Lazy Power Series
- Series Order
- Set Species
- Combinatorial Species
- Streams or Infinite Arrays
- Species structures
- Subset Species
- Sum species
- Subsets
- Subsets satisfying a hereditary property
- Subsets whose elements satisfy a predicate pairwise
- Subwords
- Subword complex
- Super Tableaux
- Super Partitions
- Symmetric Group Algebra
- Representations of the Symmetric Group
- Tableaux
- Residue sequences of tableaux
- TableauTuples
- Generalized Tamari lattices
- Tiling Solver
- Transitive ideal closure tool.
- Tuples
- Introduction to combinatorics in Sage
- Vector Partitions
- Combinatorics on Words
- Abstract word (finite or infinite)
- Word features that are imported by default in the interpreter namespace
- Alphabet
- Finite word
- Infinite word
- Lyndon words
- Word morphisms/substitutions
- Word paths
- Shuffle product of words
- Suffix Tries and Suffix Trees
- Word classes
- Fast word datatype using an array of unsigned char
- Datatypes for finite words
- Common words
- Datatypes for words defined by iterators and callables
- User-customizable options for words
- Set of words
- Yang-Baxter Graphs
- C-Finite Sequences