Some programs for finite group actions in SYMMETRICA

• All partitions of n
• All cycletypes of n
• All permutations in S_n
• All permutations in S_n in cycle notation
• All powers of a cyclic permutation
• The values of the Euler phi function
• The Cauchy Frobenius Lemma for the group C_p acting on m^p
• The conjugacy classes in S_n
• The sign of a permutation
• The cycle decomposition of a permutation
• The fixed points of a permutation
• The number of fixed points of a permutation
• The Cauchy Frobenius Lemma
• The Cauchy Frobenius Lemma using conjugacy classes
• The Cauchy Frobenius Lemma using conjugacy classes II
• Generators of some permutation groups
• The cycle type of the induced permutation on 2-sets
• The number of cycles of the induced permutation on 2-sets
• The Cauchy Frobenius Lemma on 2-sets
• The number of k-graphs with v vertices
• Orbit representatives for group actions on the domain
• Symmetry classes of mappings
• Symmetry classes of mappings II
• Symmetry classes of injective mappings
• Symmetry classes of surjective mappings
• The Bell numbers
• The Stirling first and second numbers
• The Recontre numbers
• Graphs and their complements
• The number of selfcomplementary graphs
• Cycle indices
• The cycle indices of the linear, affine or projective group
• Composition of cycle indices
• Enumeration of graphs
• List of all graphs with v vertices
• List of all graphs with v vertices and e edges
• List of all necklaces
• The number theoretic Moebius function
• Polyas Theorem
• The Lehmer code
• The reduced decomposition of a permutation
• The number of inversions of a permutation
• SYMMETRICA example files for finite group actions
• The Sims chain
• The conjugacy classes of S_m wreath S_n
• Number of partitions alpha of nm where alpha₁<=n and l(alpha)<=m
• The bruhat order
• Power series for combinatorial species
• Composition of combinatorial species