Consider the permutation D 1 2 3 4 5 6 7 8 9 2 4 1 6 5 3 8 9 7 . Please express in as

Chapter 27, Problem 27.1

(choose chapter or problem)

Consider the permutation D 1 2 3 4 5 6 7 8 9 2 4 1 6 5 3 8 9 7 . Please express in as many forms as possible, including the following: a. As a set of ordered pairs. (Never forget: A permutation is a function, and functions are sets of ordered pairs.) b. As a two-column chart. c. In cycle notation (disjoint cycle). d. As the composition of transpositions. e. As a diagram with two collections of dots for the numbers 1 through 9 (one collection on the left and one collection on the right) with arrows from left to right. f. As a diagram with one collection of dots for the numbers 1 through 9 with arrows from i to .i / for each i D 1; 2; : : : ; 9.