Integer Partitions asymptotic behaviour Let $ P(n) $ be the number of partitions of number $n$. 
Prove that $ P(n)$, grows faster than any polynomial from $n$.
I am looking for an elementary (rather bijective) proof of the fact.

The number of ordered partitions of $n$ into exactly $k$ parts is, by the usual combinatorial "stars and bars" argument, $\binom{n-1}{k-1}$: imagine placing $n$ objects in a row and adding $k-1$ dividers in the $n-1$ spaces between them.
As a result, a lower bound for the number of unordered partitions of $n$ into $k$ parts is $\frac1{k!} \binom{n-1}{k-1}$, which is $\Omega(n^{k-1})$. This is also, of course, a lower bound for $P(n)$.
The argument works for any $k$, proving that $P(n)$ grows faster than a polynomial of any degree.
