A permutation on a set can be regarded as a function from the set to itself. For
Chapter 9, Problem 47(choose chapter or problem)
A permutation on a set can be regarded as a function from the set to itself. For instance, one permutation of {1, 2, 3, 4} is 2341. It can be identified with the function that sends each position number to the number occupying that position. Since position 1 is occupied by 2, 1 is sent to 2 or 1 → 2; since position 2 is occupied by 3, 2 is sent to 3 or 2 → 3; and so forth. The entire permutation can be written using arrows as follows:
a. Use arrows to write each of the six permutations of {1, 2, 3}.
b. Use arrows to write each of the permutations of {1, 2, 3, 4} that keep 2 and 4 fixed.
c. Which permutations of {1, 2, 3} keep no elements fixed?
d. Use arrows to write all permutations of {1, 2, 3, 4} that keep no elements fixed.
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