Permute using symmetric vs alternating groups

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Asked 4 years ago

Modified 4 years ago

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Why does this happen?

Permute[{0, 0, 0}, SymmetricGroup[3]]

(* {{0, 0, 0}} *)

Permute[{0, 0, 0}, AlternatingGroup[3]]

(* {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}} *)

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asked Mar 22, 2019 at 20:19

user63582

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$\begingroup$ It would be helpful if you specified what you find surprising in these results and what results you were expecting instead. $\endgroup$
– MarcoB
Mar 22, 2019 at 21:00
$\begingroup$ Why not {{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0}} for S3 $\endgroup$
– user63582
Mar 22, 2019 at 21:03
$\begingroup$ As you can see by trying Permute[{a, a, b}, SymmetricGroup[3]] and Permute[{a, b, c}, SymmetricGroup[3]], Permute returns a list of non-identical results (essentially using something like DeleteDuplicates at the end). $\endgroup$
– march
Mar 22, 2019 at 21:54
1

$\begingroup$ @march But then, why does the AlternatingGroup[3] version have 3 identical results? I think this is probably a bug. $\endgroup$
– Carl Woll
Mar 22, 2019 at 22:13
1

$\begingroup$ @CarlWoll. Yes, you're right: that's inconsistent behavior. Some basic playing around indicates that SymmetricGroup is the outlier here. $\endgroup$
– march
Mar 22, 2019 at 22:20

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