On permutation
Posted: Thu Mar 09, 2017 12:15 pm
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 $n$.
$$D(\sigma)=\prod_{i=1}^n |i-\sigma(i)|$$
What is greater: the sum of displacements of even permutations or the sum of displacements of odd permutations? The answer may depend on $n$.