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Results tagged with symmetric-groups
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user 35416
The symmetric group $S_n$ is the group of permutations of the set of integers $\{1,\dots,n\}$. This has $n!$ elements and is generated by the $n-1$ involutions exchanging consecutive integers. The symmetric groups form the simplest family of Coxeter groups.
13
votes
Branching rule from symmetric group $S_{2n}$ to hyperoctahedral group $H_n$
This is an answer to the second question: I ran an experiment with $S_6$ (which was the best guess due to the famous "oddness" of 6). There are two subgroups in $S_6$ isomorphic to this involution cen …
- 13k
47
votes
Accepted
Roots of permutations
$\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\SL}{SL}$
The maximum of the function counting square roots is attained at $x_0=1$ and this statement generalises quite well.
Let $s(\chi)$ denote …
- 13k