ar(x) = a(r(x))
so I think you should start with r as you've done i.e. 1 -> 3 -> 6, 2 -> 6 -> 1, etc.
Product or Composite of Two Permutations
Can I ask one thing? I am really sorry.
I have a = ( 1 2 3 4 5 6 7 ) and r = (1 2 3 4 5 6 7 )
3 2 6 7 4 1 5 3 6 5 2 7 4 1
if I want to get ar = should I start with r? so 1 -> 3 -> 6 ?
or start with a?
I thought I need to start with r, but some books says it starts with a
But, those are different answers..
Please help me out.
ar(x) = a(r(x))
so I think you should start with r as you've done i.e. 1 -> 3 -> 6, 2 -> 6 -> 1, etc.
Product or Composite of Two Permutations
First of all make it readable.
There is no universal agreement of combining permutations. About one third of the sample textbooks that I reviewed say to use left/right order (that agrees with your textbook). All the rest say use function composition as in reply #2.
If I were you however, I would follow the textbook, although I personally prefer the composition way.
BTW: the authors who do the second way use the word composition, while the first way is often called product.