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Results tagged with symmetric-groups
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user 9672
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.
5
votes
Accepted
Induced representation of a Young subgroup
The answer is a special case of Young's rule. In my book, I give a very simple method for the slightly easier case where $r=0$. In that case we have:
$$
\mathrm{Ind}_{S_k\times S_l}^{S_n} = \bigoplus_ …
- 5,654
6
votes
Provoking involutions further
Define a standard bitableau of size $n$ to be a pair $(P_1, P_2)$ of standard tableaux of total size $n$ such that each of the integers $1,\dotsc, n$ occurs exactly once in either tableau.
Then $I_2( …
- 5,654
3
votes
On the symmetric group of 2^n elements
These spaces are related to $2$-Sylow subgroups of $S_n$. For example, if $n=2^k$, then $X^n_{k+1}$ is the set of $2$-Sylow subgroups of $S_n$. To see this, note that $S_n$ acts transitively on $X^n_{ …
- 5,654
2
votes
Accepted
Identity involving partitions coming from representations of alternating groups
This question got answered by Gjergji Zaimi and Richard Stanley in the comments. I simply reproduce their comments here as an answer:
A very simple explanation for this identity comes from the theory …
CommunityBot
- 1
5
votes
1
answer
346
views
Identity involving partitions coming from representations of alternating groups
It is not difficult to show that the number of conjugacy classes in the alternating group $A_n$ is given by
classes in the alternating group = no. of even partitions + no. of self-transpose partit …
CommunityBot
- 1