Question on Permutations and Products of Transpositions.

[Wesc]

Hi all, I've answered a question but there's no answer for it, and if ye could tell me if I'm doing it right I'd appreciate it thanks :)

Permutation: 1 2 3 4 5 6 7 8 9 10 11 12 13 14
--------------------2 3 1 6 5 4 8 10 13 11 12 7 14 9

(i) Write it as a product of transpositions.

I got the answer (1 2)(2 3)(4 6)(7 8)(8 10)(10 11)(11 12)(13 14)(14 9) ... But unsure if this is correct !

(ii) What is the sign of the permutation in terms of the product of transpositions? ... Not sure what the answer is here :( Could anyone show me how to do it?

 

[micromass]

Hi all, I've answered a question but there's no answer for it, and if ye could tell me if I'm doing it right I'd appreciate it thanks :)

Permutation:

1 2 3 4 5 6 7 8  9  10 11 12 13 14
2 3 1 6 5 4 8 10 13 11 12 7  14 9

(i) Write it as a product of transpositions.

I got the answer (1 2)(2 3)(4 6)(7 8)(8 10)(10 11)(11 12)(13 14)(14 9) ... But unsure if this is correct !

Seems ok.

(ii) What is the sign of the permutation in terms of the product of transpositions? ... Not sure what the answer is here :( Could anyone show me how to do it?

Is it written as a odd or an even number of permutations? What is the corresponding sign?

 

[Wesc]

Seems ok.



Is it written as a odd or an even number of permutations? What is the corresponding sign?

Obviously >.< *Facepalm*

Thank you.