Determining Missing Images in an Even Permutation

In summary, the conversation discusses a permutation in the symmetric group S9 where the images of 5 and 4 are missing, and the question is asked about what the images must be in order for the permutation to be even. The attempt at a solution suggests that X should be 5 and Y should be 4 in order to have 6 transpositions. The summary concludes with confirmation from the other participant that the solution seems logical.
  • #1
Justabeginner
309
1

Homework Statement


Hi, I have been MIA lately due to work, but I am back with questions, and eager to learn! I am self studying, and so I have inconsistencies in my learning which I hope to iron out.

Suppose you are told that the permutation
( 1 2 3 4 5 6 7 8 9
3 1 2 X Y 7 8 9 6)

In S9 the symmetric group, where the images of 5 and 4 have been lost, is an even permutation. What must the images of 5 and 4 be?


Homework Equations





The Attempt at a Solution


I thought X should be 5, and Y should be 4, so that you have 6 transpositions or am I oversimplifying the logic here?
Thank you.
 
Physics news on Phys.org
  • #2
Justabeginner said:

Homework Statement


Hi, I have been MIA lately due to work, but I am back with questions, and eager to learn! I am self studying, and so I have inconsistencies in my learning which I hope to iron out.

Suppose you are told that the permutation
( 1 2 3 4 5 6 7 8 9
3 1 2 X Y 7 8 9 6)

In S9 the symmetric group, where the images of 5 and 4 have been lost, is an even permutation. What must the images of 5 and 4 be?


Homework Equations





The Attempt at a Solution


I thought X should be 5, and Y should be 4, so that you have 6 transpositions or am I oversimplifying the logic here?
Thank you.
Looks good to me.
 
  • #3
Thank you.
 

FAQ: Determining Missing Images in an Even Permutation

1. What is a permutation?

A permutation is a rearrangement of a set of elements in a specific order. For example, if we have the set {1, 2, 3}, a permutation of this set could be {2, 1, 3}.

2. What are missing images in permutation?

Missing images in permutation refer to elements that are not included in a specific permutation. For example, if we have the set {1, 2, 3, 4} and a permutation {2, 4, 1}, the missing images would be 3.

3. How do you find missing images in permutation?

To find missing images in permutation, we need to compare the original set to the permutation. Any elements that are in the original set but not in the permutation are considered missing images.

4. Why is finding missing images important in permutation?

Finding missing images in permutation is important because it helps us understand the structure and properties of the set. It also allows us to identify patterns and make predictions about future permutations.

5. Can you have more than one missing image in a permutation?

Yes, it is possible to have more than one missing image in a permutation. The number of missing images depends on the number of elements in the original set and the specific permutation being analyzed.

Similar threads

Replies
3
Views
2K
Replies
5
Views
2K
Replies
2
Views
886
Replies
7
Views
2K
Replies
60
Views
7K
Replies
2
Views
4K
Back
Top