Doron,
You have admitted it isn't your work, and you have admitted you don't understand it. You just blindly paste into one document after another. So, what's the point? If Moshe cares to join the forum and discuss it, that would be fine, but - by your own admission - any discussion with you would be wasted.
In other words, you can't demonstrate your 10 or more errors.
Here are some of my corrections:
[latex]
\begin{table}
\begin{tabular}{ll}
First we observe the partitions of number $n$: &$\Gamma
$\\
\\
Every $\alpha \in \Gamma
$ has an inner structure: &$\alpha \equiv (a_{1}, a_{2}, a_{3},\dotsc,a_{n})$\\
&$\sum_{i=1}^{n} i a_{i} = n$\\
\\
We d efine the following function: &$g(a,b) = \frac{(a+b-1)!}{(a-1)!b!}$\\
\\
Every Partition $\alpha$ d efines different Organic &\\
Numbers $D(\alpha)$ that are calculated by the recursion: $k=n-1$ &$D(\alpha) = \prod_{i=1}^{k} g(Or(i), a_{i})$\\
\\
The value of $Or
$ is based on the following algorithm:
&$Or
= \sum_{\alpha \in \Gamma
} D(\alpha)$\\
\end{tabular}
\end{table}
[/latex]
I have added index i to a in D(alpha) equation.
I have changed index n to index k in D(alpha) equation.
Any way this is Moshe's stuff, so I am still waiting to his reply about this case,
which is, again, a minor problem that has no influence on OM's reasoning.
