 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2014-resit/12/vi/solution

Reversal has one inversion of a permutation for every pair of indices, hence

(2 n) = n (n - 1) /2

ϵ_{n, n - 1, \dots, 1} = (- 1)^{n (n - 1) /2} .

It is

+ 1

for

n \equiv 0, 1 (mod 4)

and

- 1

for

n \equiv 2, 3 (mod 4)

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