For the transposition (i j)(k), this is what I have in my

  • Thread starter Artusartos
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In summary, the transposition (i j)(k) results in k if k is not equal to i or j, i if k is not equal to j, and j if k equals i. This may seem confusing due to the use of brackets, but it is important to note that (i j)(k) is the result of the transposition (i j) being applied to the element k. It is also worth mentioning that there was a correction made to the statement regarding the result being i if k is not equal to j.
  • #1
Artusartos
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For the transposition (i j)(k), this is what I have in my notes:

[itex](i j)(k) = k[/itex] if k is not equal to i or j
[itex](i j)(k) = i[/itex] if k is not equal to j
[itex](i j)(k) = j[/itex] if k = i

My question:

I thought the product of permuations is again a permutation, but here they are just equal to numbers. Can anybody explain why?

Thanks in advance
 
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  • #2


Maybe the brackets a bit confusing, and what you(r teacher) actually meant by (i j)(k) is the result of the transposition (i j) applied to the element k?

Also,
Artusartos said:
[itex](i j)(k) = i[/itex] if k is not equal to j

Are you sure you meant "not equal"?
 
  • #3


CompuChip said:
Maybe the brackets a bit confusing, and what you(r teacher) actually meant by (i j)(k) is the result of the transposition (i j) applied to the element k?

Also,


Are you sure you meant "not equal"?

Maybe I copied that wrong. Thanks, I think I understand it now. :)
 

FAQ: For the transposition (i j)(k), this is what I have in my

What is transposition?

Transposition is a mathematical operation that involves rearranging the positions of elements in a set or sequence.

What is the format of "For the transposition (i j)(k)"?

The format of this transposition is (i j)(k), where i and j are the elements that are being swapped and k is the element that remains in place.

What does (i j)(k) mean in the context of transposition?

In (i j)(k), (i j) represents the swapping of elements i and j, while (k) indicates that element k remains in its original position.

How is transposition used in scientific research?

Transposition is commonly used in various scientific fields such as genetics, chemistry, and physics to rearrange and analyze data, sequences, and structures.

What is the purpose of the transposition (i j)(k) in scientific research?

The purpose of this transposition is to manipulate and analyze data in a way that allows for better understanding and interpretation of patterns and relationships between elements.

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