Permutation representation
Permutation representation is like a way to show how things can be arranged or shuffled around. Imagine you have a bunch of toys on the floor, and you want to see how many different ways you can arrange them. You might put a toy car next to a stuffed animal, or put a teddy bear on top of a dollhouse. Each of those arrangements is a different permutation, or way of arranging the toys.
Now let's say you want to keep track of all those different arrangements in a organized way. That's where permutation representation comes in. You can assign a number to each toy, like 1 for the car, 2 for the stuffed animal, and so on. Then you can write down each permutation as a list of those numbers, showing where each toy is located. So one permutation might be (1,3,2,4), meaning the car is in spot number 1, the teddy bear is in spot 3, the stuffed animal is in spot 2, and the dollhouse is in spot 4.
You can also use special symbols to show the different permutations. For example, (12) might mean swapping toys 1 and 2, so if you started with (1,2,3,4), you'd end up with (2,1,3,4). Or (123) might mean rotating the toys so that the first three move one spot to the right, like starting with (1,2,3,4) and ending up with (4,1,2,3).
Overall, permutation representation is just a way of organizing and keeping track of all the different ways things can be arranged or shuffled around.
Now let's say you want to keep track of all those different arrangements in a organized way. That's where permutation representation comes in. You can assign a number to each toy, like 1 for the car, 2 for the stuffed animal, and so on. Then you can write down each permutation as a list of those numbers, showing where each toy is located. So one permutation might be (1,3,2,4), meaning the car is in spot number 1, the teddy bear is in spot 3, the stuffed animal is in spot 2, and the dollhouse is in spot 4.
You can also use special symbols to show the different permutations. For example, (12) might mean swapping toys 1 and 2, so if you started with (1,2,3,4), you'd end up with (2,1,3,4). Or (123) might mean rotating the toys so that the first three move one spot to the right, like starting with (1,2,3,4) and ending up with (4,1,2,3).
Overall, permutation representation is just a way of organizing and keeping track of all the different ways things can be arranged or shuffled around.