question on permutations. suppose we have the sequence 1,2,3,4 and we do a permutation on it to get 4,1,2,3 . So my question is, there are two ways we can define the permutation. we can say that 1 is sent to the 2 place, 2 is sent to the 3 place, 3 is sent to the 4 place and 4 is sent to the 1 place. Or, we can define it f(1) = 4, f(2) = 1, f(3) = 2, f(4)=3.

Question

question on permutations. suppose we have the sequence 1,2,3,4 and we do a permutation on it to get 4,1,2,3  . So my question is, there are two ways we can define the permutation. we can say that 1 is sent to the 2 place, 2 is sent to the 3 place, 3 is sent to the 4 place  and 4 is sent to the 1 place. Or, we can define it f(1) = 4, f(2) = 1, f(3) = 2, f(4)=3.

kinggeorge · Answer

Those two ways should be equally valid as long as it is clear exactly how the functions are working.

kinggeorge · Answer

From my understanding, one function is permuting the numbers, and the other function is permuting the labels of the positions.

perl · Answer

sorry , i was afk

perl · Answer

starting with 1,2,3,4 ->  4,1,2,3 
you could say 1 is moved to where the 2 use to be, 2 moved to where 3 use to be, 3 moves to where 4 use to be 
or we could say f(1) = 4 , f(2) = 1 , f(3) = 2, etc

kinggeorge · Answer

Right. The first way is permuting the numbers, and the second way is saying "The first spot gets the number 4, the second gets the number 1,..." 

You only really see differences when you start composing permutations together. 

I too will be afk for a bit here.

perl · Answer

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