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# `SG` - library for the symmetric group

## Table of contents

1. The library `muEC::SG`

1. `Code2Perm` - calculates a permutation from its code
2. `CompPerm` - compares two permutations
3. `Cycle2Perm` - calculates the permutation from its decomposition into disjoint cycles
4. `Desc2ListPerm` - generates all permutations with a given descent set
5. `FactorPerm` - tests whether a permutation factorizes into a direct product
6. `GenPerm` - generates an element of the symmetric group
7. `ListPerm` - generates all permutations
8. `Mat2Perm` - calculates a permutation from its matrix
9. `MultPerm` - multiply permutations
10. `Part2SgCC` - computes a conjugacy class of the symmetric group
11. `Perm2Betti` - computes the Betti polynomial
12. `Perm2Code` - calculates the code of a permutation
13. `Perm2CycleType` - computes the cycle type of a permutation
14. `Perm2Cycle` - decomposes a permutation into disjoint cycles
15. `Perm2Desc` - computes the list of descents of a permutation
16. `Perm2Interval` - computes all codes of permutations below a given one
17. `Perm2Inv` - inverts a permutation
18. `Perm2Length` - calculates the length of a permutation
19. `Perm2ListInv` - calculates the set of inversions of a permutation
20. `Perm2ListRd` - lists all reduced decompositions of a given permutation
21. `Perm2Mat` - calculates the permutation matrix
22. `Perm2RRep` - calculates the matrix representing a permutation in the regular representation
23. `Perm2Rd` - calculates a canonical reduced decomposition of a permutation
24. `Perm2Rise` - computes the list of rises of a permutation
25. `Perm2Rothe` - calculates the Rothe diagram of a permutation
26. `Perm2Sign` - returns the signature of a permutation
27. `RRep2Perm` - calculates a permutation from its matrix in the regular representation
28. `RandPerm` - returns a random permutation
29. `Rd2Perm` - calculates a permutation from a decomposition
30. `SgCharTable` - computes the table of characters
31. `SgDimRep` - computes the dimension of a representation
32. `SgTranspo` - returns a transposition
33. `Vect2Perm` - computes a canonical permutation from a vector

[Contents]

MuPAD Combinat, an open source algebraic combinatorics package