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 Post subject: On permutation
PostPosted: Thu Mar 09, 2017 12:15 pm 

Joined: Sat Nov 14, 2015 6:32 am
Posts: 132
Location: Melbourne, Australia
For any permutation $\sigma:\{1,2,\dots,n\}\to\{1,2,\dots,n\}$ define its displacement as

$$D(\sigma)=\prod_{i=1}^n |i-\sigma(i)|$$

What is greater: the sum of displacements of even permutations or the sum of displacements of odd permutations? The answer may depend on $n$.

_________________
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$


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