# Solution: 2020-09 Displacement of permutations

For a permutation $$\pi: [n]\rightarrow [n]$$, we define the displacement of $$\pi$$ to be $$\sum_{i\in [n]} |i-\pi(i)|$$.

For given $$k$$, prove that the number of even permutations of $$[n]$$ with displacement $$2k$$ minus the number of odd permutations of $$[n]$$ with displacement $$2k$$ is $$(-1)^{k}\binom{n-1}{k}$$.

The best solution was submitted by 홍의천 (수리과학과 2017학번). Congratulations!

Here is his solution of problem 2020-09.

Another solution was submitted by 고성훈 (수리과학과 2018학번, +3).

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