I want to calculate (or approximate) this convolution.
$$ f_n(x)=(1-x)^n*(1-x)^{n-1}*...*(1-x) $$ $$0<x<1$$
and the goal is to calculate this integration.
$$ \int_{0}^{1} f_n(t)dt$$
I think it must be an application of Fourier transform.
The original problem is to find $$\min_{\sigma}{(\sum_{i=1}^{n} a_{i\sigma(i)})}$$ in matrix $A=[a_{ij}]_{n\times n}$ with uniformly random entries from $[0,1]$.