# Thread: permutations - help me understand please!

1. ## permutations - help me understand please!

ok.. so I have two permutations:

sigma 1:

1->3, 2->2, 3->4, 4->1

sigma 2:
1->3, 2->4, 3->1, 4->2

so sigma 1 = (1,3,4)
sigma 2 = (1,3)(2,4)

now find the compositions of sigma1sigma2
and sigma2sigma1

How do I do this?! I really dont understand which map you follow so to speak

many thanks

2. Originally Posted by James0502
ok.. so I have two permutations:

sigma 1:

1->3, 2->2, 3->4, 4->1

sigma 2:
1->3, 2->4, 3->1, 4->2

so sigma 1 = (1,3,4)
sigma 2 = (1,3)(2,4)

now find the compositions of sigma1sigma2
and sigma2sigma1

How do I do this?! I really dont understand which map you follow so to speak

many thanks
$\displaystyle \sigma_1 \sigma_2=(1,3,4)(1,3)(2,4)$

Now lets simplify this by computing the permutation.

so lets immagine sending 1 in on the right ...
1 goes through (2,4) unchanaged.
1 goes into (1,3) and comes out 3
3 goes into (1,3,4) and comes out 4

so 1 goes to 4 (1,4

Now lets send 4 in

4 goes into (2,4) and comes out 2
2 goes into (1,3) and is unchanged.
2 goes into (1,3,4) and is unchanges

so 4 goes to 2 (1,4,2

Now lets send 2 in

2 goes into (2,4) and comes out 4
4 goes into (1,3) and is unchanged
4 goes into (1,3,4) and comes out 1

so 2 goes to 1 (1,4,2)

Now the only number we didn't check in are chain is 3.

if you check it 3 goes to 3.

so we end up with

$\displaystyle \sigma_1 \sigma_2=(1,3,4)(1,3)(2,4)=(1,4,2)$

3. Originally Posted by TheEmptySet
$\displaystyle \sigma_1 \sigma_2=(1,3,4)(1,3)(2,4)$
While I agree that this is the mathematical correct to consider compositions of the permutation mappings, unfortunately there textbooks/authors that do not use this convention, they use left-to-right composition. So please check the definition of the textbook used.