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Section 21.2 Definition
We often want to count how many ways we can “mix up” the objects in a collection.
permutation
a bijection from a finite set to itself
Example 21.2.2 . Permutations of three objects.
Figure 21.2.3 contains tables of values for all six possible permutations of the set
\(A = \{a,b,c\} \text{.}\) We have grouped them according to: all elements fixed; one element fixed and two mixed; all elements mixed.
\(x \) \(a \) \(b \) \(c \)
\(\id_A(x) \) \(a \) \(b \) \(c \)
\(x \) \(a \) \(b \) \(c \)
\(f_a(x) \) \(a \) \(c \) \(b \)
\(f_b(x) \) \(c \) \(b \) \(a \)
\(f_c(x) \) \(b \) \(a \) \(c \)
\(x \) \(a \) \(b \) \(c \)
\(s_r(x) \) \(c \) \(a \) \(b \)
\(s_l(x) \) \(b \) \(c \) \(a \)
Figure 21.2.3. All possible permutations on three objects.
