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 36466
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.
3
votes
Generating symmetric groups with small cycles
Let $p$ be the smallest prime divisor of $n$. I believe that $f(n)=n/p+1$. The key points are as follows.
1) If $H \leq S_n$ is primitive and contains a $2$-cycle, then $H=S_n$.
2) If $1<k \leq m< …
- 3,571
8
votes
Accepted
Tensor products of permutation representations of symmetric groups.
Hi Dev,
It looks to me like a proof of this fact is given in the answer to Exercise 7.84(b) of Richard Stanley's Enumerative Combinatorics, volume 2, along with a reference to Example I.7.23(e), page …
- 3,571
16
votes
Accepted
Dimension of Specht Modules $S^\lambda$
The opposite is true. It is a result of D. Craven, settling a conjecture of A. Moreto, that given any $k$, for all large enough $n$, there are at least $k$ distinct irreducible representations of $S_ …
- 3,571
7
votes
A general formula for the number of conjugacy classes of $\mathbb{S}_n \times \mathbb{S}_n$ ...
I don't know that it is of the type you wish, but there is a formula of sorts.
Consider the more general case of a finite group $G$ acting diagonally by conjugation on the set of $k$-tuples of elemen …
- 3,571
6
votes
Accepted
Combinatorial problem in $\mathsf{S}_4$
Please allow me to substitute as follows in order to avoid typos: $r_{11}=a$, $r_{12}=b$, $r_{21}=c$, $r_{22}=d$, $t_{21}=e$, $t_{22}=f$.
Upon examining the character tables of $S_4$, $A_4$, and $D_8$ …
- 3,571