muEC::SG – mu-EC library for the symmetric group (package Combinat, deprecated)

The muEC::SG library provides functions to work with the symmetric group.

1. Help files

muEC::SG::Code2Perm – calculates a permutation from its code

muEC::SG::CompPerm – compares two permutations

muEC::SG::Cycle2Perm – calculates the permutation from its decomposition into disjoint cycles

muEC::SG::Desc2ListPerm – generates all permutations with a given descent set

muEC::SG::FactorPerm – tests whether a permutation factorizes into a direct product

muEC::SG::GenPerm – generates an element of the symmetric group

muEC::SG::ListPerm – generates all permutations

muEC::SG::Mat2Perm – calculates a permutation from its matrix

muEC::SG::MultPerm – multiply permutations

muEC::SG::Part2SgCC – computes a conjugacy class of the symmetric group

muEC::SG::Perm2Betti – computes the Betti polynomial

muEC::SG::Perm2Code – calculates the code of a permutation

muEC::SG::Perm2CycleType – computes the cycle type of a permutation

muEC::SG::Perm2Cycle – decomposes a permutation into disjoint cycles

muEC::SG::Perm2Desc – list of descents of a permutation

muEC::SG::Perm2Interval – computes all codes of permutations below a given one

muEC::SG::Perm2Inv – inverts a permutation

muEC::SG::Perm2Length – calculates the length of a permutation

muEC::SG::Perm2ListInv – The inversions of a permutation

muEC::SG::Perm2ListRd – lists all reduced decompositions of a given permutation

muEC::SG::Perm2Mat – calculates the permutation matrix

muEC::SG::Perm2RRep – calculates the matrix representing a permutation in the regular representation

muEC::SG::Perm2Rd – calculates a canonical reduced decomposition of a permutation

muEC::SG::Perm2Rise – the list of rises of a permutation

muEC::SG::Perm2Rothe – calculates the Rothe diagram of a permutation

muEC::SG::Perm2Sign – returns the signature of a permutation

muEC::SG::RRep2Perm – calculates a permutation from its matrix in the regular representation

muEC::SG::RandPerm – random permutation

muEC::SG::Rd2Perm – permutation from a decomposition

muEC::SG::SgCharTable – the character table

muEC::SG::SgDimRep – computes the dimension of a representation

muEC::SG::SgTranspo – returns a transposition

muEC::SG::Vect2Perm – computes a canonical permutation from a vector