σ(1) {1,2,3,4,5,6,7}σ(1) = 6
σ(2) {1,2,3,4,5,7}
σ(2) = 3
•
•
•n
•
n
σ{1,...,n}
i∈ {1,...,n}σ(σ(i)) = i i ∈ {1,...,n}σ(i)6=i
σ{1,...,n}S S[i−1] = σ(i)
i∈ {1,...,n}
{1,...,4}
[1,2,3,4] [2,1,4,3] [4,3,2,1] [1,3,2,4]
n>0S
σ{1, . . . , n}1σ0
n>0
{1,...,n}
{1,...,n}n
?
n
n(n−1)(n−3) · · · 1 = (n−1)!
2(n/2−1)! 0
σ{1,...,n}k k
ka1, . . . , ak{1,...,n}σ(ai) = ai+1 i∈ {1,...,k−1}
σ(ak) = a1j /∈ {a1, . . . , an}σ(j) = j
k∈ {2, . . . , n}k
σ{1,...,n}S S[i−1] = σ(i)
i∈ {1,...,n}
{1,2,3,4}
n>0 2
{1, . . . , n}