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Combinatorics¶

Contents¶

  • Partitions
    • Partition
    • IntegerPartition
    • random_integer_partition()
    • RGS_generalized()
    • RGS_enum()
    • RGS_unrank()
    • RGS_rank()
  • Permutations
    • Permutation
    • Cycle
    • _af_parity()
    • Generators
  • Permutation Groups
    • PermutationGroup
  • Polyhedron
    • Polyhedron
  • Prufer Sequences
    • Prufer
  • Subsets
    • Subset
    • subsets.ksubsets()
  • Gray Code
    • GrayCode
    • graycode.random_bitstring()
    • graycode.gray_to_bin()
    • graycode.bin_to_gray()
    • graycode.get_subset_from_bitstring()
    • graycode.graycode_subsets()
  • Named Groups
    • SymmetricGroup()
    • CyclicGroup()
    • DihedralGroup()
    • AlternatingGroup()
    • AbelianGroup()
  • Utilities
    • _base_ordering()
    • _check_cycles_alt_sym()
    • _distribute_gens_by_base()
    • _handle_precomputed_bsgs()
    • _orbits_transversals_from_bsgs()
    • _remove_gens()
    • _strip()
    • _strong_gens_from_distr()
  • Group constructors
    • DirectProduct()
  • Test Utilities
    • _cmp_perm_lists()
    • _naive_list_centralizer()
    • _verify_bsgs()
    • _verify_centralizer()
    • _verify_normal_closure()
  • Tensor Canonicalization
    • canonicalize()
    • double_coset_can_rep()
    • get_symmetric_group_sgs()
    • bsgs_direct_product()
  • Finitely Presented Groups
    • Introduction
    • The Construction of Finitely Presented Groups
    • Free Groups and Words
    • Coset Enumeration: The Todd-Coxeter Algorithm
    • Subgroups of Finite Index
    • Constructing a presentation for a subgroup
    • Bibliography
  • Polycyclic Groups
    • Introduction
    • The Construction of Polycyclic Groups
    • The Construction of Collector
    • Computation of Polycyclic Presentation
    • Computation of Exponent Vector
    • Bibliography

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