Combinatorics

• Combinatorial Functions.
• Functions that compute some of the sequences in Sloane’s tables
• Compute Bell and Uppuluri-Carpenter numbers.
• Alternating Sign Matrices
• Cartesian Products
• Combinations
• Signed Compositions
• Integer compositions
• Exact Cover Problem via Dancing Links
• Dancing links C++ wrapper
• Dyck Words
• Finite combinatorial classes
• Tools for generating lists of integers in lexicographic order.
• Integer vectors
• Weighted Integer Vectors
• Restricted growth arrays
• Yamanouchi Words
• Paths in Directed Acyclic Graphs
• Latin Squares
• Lyndon words
• Necklaces
• Non-Decreasing Parking Functions
• Partitions
• Permutations
• Perfect matchings
• q-Analogues
• Ordered Set Partitions
• Set Partitions
• Skew Partitions
• Subsets
• Subwords
• Tuples
• Combinatorial Algebras
  • Free modules
  • Combinatorial Algebras
  • Symmetric Group Algebra
  • Schubert Polynomials
  • Partition/Diagram Algebras
  • Iwahori Hecke Algebras
• Tableaux and Tableaux-like Objects
  • Tableaux
  • Skew Tableaux
  • Ribbons
  • Ribbon Tableaux
• Symmetric Functions
  • Symmetric Functions
  • Classical symmetric functions.
  • Schur symmetric functions
  • Monomial symmetric functions
  • Multiplicative symmetric functions
  • Elementary symmetric functions
  • Homogenous symmetric functions
  • Power-sum symmetric functions
  • Generic dual bases symmetric functions
  • Symmetric functions defined by orthogonality and triangularity.
  • Kostka-Foulkes Polynomials
  • Hall-Littlewood Polynomials
  • Jack Polynomials
  • k-Schur Functions
  • LLT Polynomials
  • Macdonald Polynomials
  • Non-symmetric Macdonald Polynomials
• Root Systems
  • Cartan types
  • Dynkin diagrams
  • Cartan matrices
  • Coxeter matrices
  • Root systems
  • Weyl Groups
  • Weyl Characters
• Kazhdan-Lusztig Polynomials
• Crystals
  • Affine Crystals
  • Crystals
  • Direct Sum of Crystals
  • Crystals of letters
  • Fast Rank Two Crystals
  • Highest weight crystals
  • Affine crystals
  • Spin Crystals
  • Tensor Products of Crystals
• Posets
  • Posets
  • Hasse diagrams of posets
  • Elements of posets, lattices, semilattices, etc.
  • SemiLattices and Lattices
  • Some examples of posets and lattices.
• Designs and Incidence Structures
  • Block designs.
  • External Representations of Block Designs
  • Incidence structures.
• Combinatorial Species
  • Power Series
  • Basic Species
  • Operations on Species
  • Miscellaneous
• Developer Tools
  • Backtracking
  • Output functions
  • Low-level permutations
  • Low-level splits
  • Low-level Combinations
  • Low-level multichoose
  • Tools
  • Generators
  • Rankers
• Words
  • Alphabets
  • Abstract word (finite or infinite)
  • Finite word
  • Infinite word
  • Word classes
  • A collection of constructors of common words
  • Combinatorial classes of words.
  • Shuffle product of words
  • Suffix Tries and Suffix Trees
  • Word morphisms/substitutions
  • Word paths
  • Word utilities (DEPRECATED)
  • Word contents (DEPRECATED)
• Interval exchange transformations and linear involutions
  • Class factories for Interval exchange transformations.
  • Strata of differentials on Riemann surfaces
  • Labelled permutations
  • Reduced permutations
  • Permutations template
  • Interval Exchange Transformations and Linear Involution
• Miscellaneous