File:Symmetric group S4; conjugacy table.svg
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Summary[edit]
DescriptionSymmetric group S4; conjugacy table.svg |
The numbers represent the permutations of 4 elements in reverse colexicographic order (compare Symmetric group S4). In the position this table shows the result of (
In terms of left action, usual as function composition, this would be .
The leftmost column serves as a vertical index. To the left the matrices of the permutations are shown. The second horizontal index (semi-transparent) shows the inverse permutations of those in the main index Example: () >>> from sympy.combinatorics import Permutation >>> Permutation.print_cyclic = False >>> a = Permutation([0, 1, 3, 2]) >>> b = Permutation([3, 0, 2, 1]) >>> a^b Permutation[0, 2, 1, 3] >>> ~b*a*b Permutation[0, 2, 1, 3] Calculation of the matrix with Python: http://pastebin.com/BGkvfdgH (as
The positions of permutations with inversion sets symmetric to each other have positions in the table that are symmetric to each other. |
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