Comprehensive module list¶
sage.combinat¶
- A bijectionist’s toolkit
- Abstract recursive trees
- Affine permutations
- Algebraic combinatorics
- Alternating sign matrices
- Backtracking
- Baxter permutations
- Bell and Uppuluri-Carpenter numbers
- Binary recurrence sequences
- Binary trees
- Blob algebras
- Boundedness of \(k\)-Regular Sequences
- Brent Yorgey’s fast algorithm for integer vector (multiset) partitions
- Cartesian products
- Cluster complex (or generalized dual associahedron)
- Colored permutations
- Combinations
- Combinatorial diagrams
- Combinatorial functions
- Combinatorial maps
- Combinatorial triangles for posets and fans
- Combinatorics
- Introduction to combinatorics in Sage
- Combinatorics quickref
- Common automata and transducers (finite state machines generators)
- Composition tableaux
- Constellations
- Cores
- Counting
- Counting, generating, and manipulating nonnegative integer matrices
- Cyclic sieving phenomenon
- De Bruijn sequences
- Decorated permutations
- Degree sequences
- Derangements
- Descent algebras
- Diagram and partition algebras
- Dyck words
- Enumerated sets
- Exact cover problem via dancing links
- Families
- Fast computation of combinatorial functions (Cython + mpz)
- Fast set partition iterators
- Finite state machines, automata, transducers
- Free dendriform algebras
- Free modules
- Free pre-Lie algebras
- Free quasi-symmetric functions
- Fully commutative elements of Coxeter groups
- Fully packed loops
- Functions that compute some of the sequences in Sloane’s tables
- Gelfand-Tsetlin patterns
- Generalized Tamari lattices
- Gray codes
- Grossman-Larson Hopf algebras
- Growth diagrams and dual graded graphs
- Hall polynomials
- Integer compositions
- Integer partitions
- Integer vectors modulo the action of a permutation group
- Iterators over the partitions of an integer
- Kazhdan-Lusztig polynomials
- Key polynomials
- Kleshchev partitions
- Knutson-Tao puzzles
- Littlewood-Richardson tableaux
- Miscellaneous
- Necklaces
- Non-decreasing parking functions
- Nonnegative integer vectors
- Ordered multiset partitions into sets and the minimaj crystal
- Ordered rooted trees
- Ordered set partitions
- Output functions
- Parallelogram polyominoes
- Parking functions
- Partition shifting algebras
- Partition tuples
- Partition/diagram algebras
- Partitions, tableaux, and others
- Paths in directed acyclic graphs
- Perfect matchings
- Permutations
- Permutations (Cython file)
- Plane partitions
- Rankers
- Recognizable series
- Representations of the symmetric group
- Residue sequences of tableaux
- Restricted growth arrays
- Ribbon shaped tableaux
- Ribbon tableaux
- Ribbons
- Robinson-Schensted-Knuth correspondence
- Rooted (unordered) trees
- Schubert polynomials
- Set partitions
- Shard intersection order
- Shifted primed tableaux
- Shuffle product of iterables
- Sidon sets and their generalizations, Sidon \(g\)-sets
- Signed compositions
- Similarity class types of matrices with entries in a finite field
- Six vertex model
- Skew partitions
- Skew tableaux
- Specht modules
- Steinhaus-Johnson-Trotter algorithm
- Strong and weak tableaux
- Subsets
- Subsets satisfying a hereditary property
- Subsets whose elements satisfy a predicate pairwise
- Substitutions over unit cube faces (Rauzy fractals)
- Subword complex
- Subword complex: auxiliary Cython functions
- Subwords
- Super partitions
- Super tableaux
- Symmetric group algebra
- T-sequences
- TableauTuples
- Tableaux
- Tamari Interval-posets
- The Hillman-Grassl correspondence
- Tiling solver
- Tools for enumeration modulo the action of a permutation group
- Transitive ideal closure tool
- Tuples
- Vector partitions
- Weighted integer vectors
- Yang-Baxter Graphs
- \(\nu\)-Dyck words
- \(\nu\)-Tamari lattice
- \(k\)-regular sequences
- \(q\)-Bernoulli numbers and polynomials
- \(q\)-analogues
- sine-Gordon Y-system plotter
sage.combinat.chas¶
sage.combinat.cluster_algebra_quiver¶
sage.combinat.crystals¶
- Affine crystals
- Affine factorization crystal of type \(A\)
- Affinization crystals
- Alcove paths
- An introduction to crystals
- Benkart-Kang-Kashiwara crystals for the general-linear Lie superalgebra
- Catalog of crystal models For \(B(\infty)\)
- Catalog of crystal models for Kirillov-Reshetikhin crystals
- Catalog of crystals
- Catalog of elementary crystals
- Crystal of Bernstein-Zelevinsky multisegments
- Crystal of Mirković-Vilonen polytopes
- Crystals
- Crystals of Kac modules of the general-linear Lie superalgebra
- Crystals of generalized Young walls
- Crystals of letters
- Crystals of modified Nakajima monomials
- Direct sum of crystals
- Elementary crystals
- Fast rank two crystals
- Fully commutative stable Grothendieck crystal
- Highest weight crystals
- Induced crystals
- Kirillov-Reshetikhin crystals
- Kyoto path model for affine highest weight crystals
- Littelmann paths
- PBW data
- Polyhedral realization of \(B(\infty)\)
- Spin crystals
- Star-crystal structure on \(B(\infty)\)
- Subcrystals
- Tensor products of crystal elements
- Tensor products of crystals
- Virtual crystals
- \(\mathcal{B}(\infty)\) crystal of PBW monomials
- \(\mathcal{B}(\infty)\) crystals of tableaux in nonexceptional types and \(G_2\)
sage.combinat.designs¶
- Balanced incomplete block designs (BIBD)
- Block designs
- Bounds on the number of mutually orthogonal Latin squares
- Catalog of designs
- Combinatorial designs and incidence structures
- Covering arrays
- Covering designs: coverings of \(t\)-element subsets of a \(v\)-set by \(k\)-sets
- Cython functions for combinatorial designs
- Database of generalised quadrangles with spread
- Database of small combinatorial designs
- Difference families
- Difference matrices
- Evenly distributed sets in finite fields
- External representations of block designs
- Group-divisible designs (GDD)
- Hypergraph isomorphic copy search
- 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)
- Resolvable balanced incomplete block design (RBIBD)
- Steiner quadruple systems
- Two-graphs
sage.combinat.integer_lists¶
sage.combinat.matrices¶
sage.combinat.ncsf_qsym¶
sage.combinat.ncsym¶
sage.combinat.path_tableaux¶
sage.combinat.posets¶
- Bubble and Shuffle lattices
- Cartesian products of posets
- Catalog of posets and lattices
- D-complete posets
- Elements of posets, lattices, semilattices, etc.
- Fast linear extension iterator
- Finite lattices and semilattices
- Finite posets
- Forest posets
- Hasse diagrams of posets
- Hochschild lattices
- Incidence algebras
- Linear extensions of posets
- Mobile posets
- Möbius algebras
- Posets
- Some fast computations for finite posets
- Some fast computations for finite posets using FLINT matrices
sage.combinat.rigged_configurations¶
- Abstract classes for the rigged configuration bijections
- Bijection between rigged configurations and KR tableaux
- Bijection between rigged configurations for \(B(\infty)\) and marginally large tableaux
- Bijection classes for type \(A_n^{(1)}\)
- Bijection classes for type \(A_{2n-1}^{(2)}\)
- Bijection classes for type \(A_{2n}^{(2)\dagger}\)
- Bijection classes for type \(A_{2n}^{(2)}\)
- Bijection classes for type \(B_n^{(1)}\)
- Bijection classes for type \(C_n^{(1)}\)
- Bijection classes for type \(D_4^{(3)}\)
- Bijection classes for type \(D_n^{(1)}\)
- Bijection classes for type \(D_{n+1}^{(2)}\)
- Bijection classes for type \(E_{6,7}^{(1)}\)
- Crystal of rigged configurations
- Kirillov-Reshetikhin tableaux
- Kleber trees
- Rigged configuration elements
- Rigged configurations
- Rigged configurations
- Rigged configurations of \(\mathcal{B}(\infty)\)
- Rigged partitions
- Tensor product of Kirillov-Reshetikhin tableaux
- Tensor product of Kirillov-Reshetikhin tableaux elements
sage.combinat.root_system¶
- 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
- Extended affine Weyl groups
- Finite complex reflection groups
- Finite real reflection groups
- Fundamental group of an extended affine Weyl group
- Group algebras of root lattice realizations
- Hecke algebra representations
- Integrable representations of affine Lie algebras
- Nonsymmetric Macdonald polynomials
- Pieri factors
- Reflection group elements
- Reflection groups: auxiliary Cython functions
- Root lattice realizations
- Root lattices and root spaces
- Root system data for (untwisted) type A affine
- Root system data for (untwisted) type B affine
- Root system data for (untwisted) type C affine
- Root system data for (untwisted) type D affine
- Root system data for (untwisted) type E affine
- Root system data for (untwisted) type F affine
- Root system data for (untwisted) type G affine
- Root system data for Cartan types with marked nodes
- Root system data for affine Cartan types
- Root system data for dual Cartan types
- Root system data for folded Cartan types
- Root system data for reducible Cartan types
- Root system data for relabelled Cartan types
- Root system data for super type A
- Root system data for type A
- Root system data for type A infinity
- Root system data for type B
- Root system data for type BC affine
- Root system data for type C
- Root system data for type D
- Root system data for type E
- Root system data for type F
- Root system data for type G
- Root system data for type H
- Root system data for type I
- Root system data for type Q
- Root systems
- Root systems
- Tutorial: visualizing root systems
- Weight lattice realizations
- Weight lattices and weight spaces
- Weyl character rings
- Weyl groups
sage.combinat.sf¶
- Abreu-Nigro symmetric functions
- Characters of the symmetric group as bases of the symmetric functions
- Classical symmetric functions
- Elementary symmetric functions
- Generic dual bases symmetric functions
- Hall-Littlewood polynomials
- Hecke character basis
- Homogeneous symmetric functions
- Jack symmetric functions
- Kostka-Foulkes polynomials
- LLT symmetric functions
- Macdonald polynomials
- Monomial symmetric functions
- Multiplicative symmetric functions
- Non-symmetric Macdonald polynomials
- Orthogonal symmetric functions
- Power sum symmetric functions
- Quotient of symmetric function space by ideal generated by Hall-Littlewood symmetric functions
- Schur symmetric functions
- Symmetric functions
- Symmetric functions
- Symmetric functions defined by orthogonality and triangularity
- Symmetric functions, with their multiple realizations
- Symplectic symmetric functions
- Witt symmetric functions
- \(k\)-Schur functions
sage.combinat.species¶
- Characteristic species
- Combinatorial species
- Combinatorial species
- Composition species
- Cycle species
- Empty species
- Examples of combinatorial species
- Functorial composition species
- Generating series
- Linear-order species
- Miscellaneous functions
- Partition species
- Permutation species
- Product species
- Recursive species
- Set species
- Species structures
- Subset species
- Sum species
sage.combinat.words¶
- Abstract word (finite or infinite)
- Alphabet
- Combinatorics on words
- Common words
- Datatypes for finite words
- Datatypes for words defined by iterators and callables
- Fast word datatype using an array of unsigned char
- Finite word
- Infinite word
- Lyndon words
- Morphic words
- Set of words
- Shuffle product of words
- Suffix tries and suffix trees
- User-customizable options for words
- Word classes
- Word morphisms/substitutions
- Word paths
See also¶
Note
This list was initially created by executing in a Sage shell (sage -sh):
$ src/doc/en/reference/make_module_list.sh sage/combinat
The result was copy-pasted here, grouped by package.