Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with symmetric-groups
Search options not deleted
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.
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 …
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 …
- 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
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