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()
• Nilpotent, Abelian and Cyclic Numbers
  • is_nilpotent_number()
  • is_abelian_number()
  • is_cyclic_number()
• 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