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When I am trying to compute some products of permutations in S_48, it is somehow not working.

Here is my code:

PermutationProduct[{Cycles[{{40, 35, 33, 38}, {37, 34, 36, 39}, {46, 3, 19, 27}, {44, 5, 21, 29}, {41, 8, 24, 32}}], 
Cycles[{{43, 41, 46, 48}, {42, 44, 47, 45}, {1, 35, 32, 14}, {2, 37, 31, 12}, {3, 40, 30, 9}}]}]

But it gives:

{Cycles[{{3, 19, 27, 46}, {5, 21, 29, 44}, {8, 24, 32, 41}, {33, 38, 
40, 35}, {34, 36, 39, 37}}], Cycles[{{1, 35, 32, 14}, {2, 37, 31, 12}, {3, 40, 30, 9}, {41, 46, 
48, 43}, {42, 44, 47, 45}}]}

which is literally the same, but it is definitely not it.

Also, when I am doing:

PermutationOrder[{Cycles[{{3, 19, 27, 46}, {5, 21, 29, 44}, {8, 24, 32, 41}, {33, 38, 40, 35}, {34, 36, 39, 37}}], Cycles[{{1, 35, 32, 14}, {2, 37, 31, 12}, {3, 40, 30, 9}, {41, 46, 48, 43}, {42, 44, 47, 45}}]}]

It yields:

PermutationOrder[{Cycles[{{3, 19, 27, 46}, {5, 21, 29, 44}, {8, 24, 
 32, 41}, {33, 38, 40, 35}, {34, 36, 39, 37}}], Cycles[{{1, 35, 32, 14}, {2, 37, 31, 12}, {3, 40, 30, 9}, {41, 46, 
 48, 43}, {42, 44, 47, 45}}]}]

which is literally the same as well!!!

Can someone help to point out the mistakes I made? I use Mathematica 12.1

Nick Yin
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    Welcome to MMA SE! The syntax for PermutationProduct is PermutationProduct[a, b, ...], not PermutationProduct[{a, b, ...}]—it takes in multiple arguments, not a single argument that's a list. Try PermutationProduct[Cycles[{{40, 35, 33, 38}, {37, 34, 36, 39}, {46, 3, 19, 27}, {44, 5, 21, 29}, {41, 8, 24, 32}}], Cycles[{{43, 41, 46, 48}, {42, 44, 47, 45}, {1, 35, 32, 14}, {2, 37, 31, 12}, {3, 40, 30, 9}}]]. (If you have a list of cycles a = {Cycle[...], Cycle[...], ...}, you can use PermutationProduct @@ a to replace the List head.) – thorimur Oct 11 '21 at 07:16
  • OHHHHHH it is working!!! – Nick Yin Oct 11 '21 at 07:33
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    Thank you haha! – Nick Yin Oct 11 '21 at 07:33
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    No problem! FYI this question will likely be closed because it was a syntax error and isn't "looking for an answer" anymore, but don't let that discourage you from asking more questions—it's just standard site practice :) – thorimur Oct 11 '21 at 07:43

0 Answers0