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I want to formally describe an algorithm $f : E \times P \to P$ which you can use as an argument for itself. Right now, I have the following definition:

\begin{equation} \begin{split} P_{e_{n+1}} &= f(e_n, P_{e_n}) \\ &= f(e_n, f(e_{n-1}, f(e_{n-2}, \dots f(e_1, P_{e_1})))) \end{split} \end{equation}

The formula should show that you only need one initial $P_{e_1} \in P$ and a set of elements $e_{x} \in E$ to generate $P_{e_{n+1}}$. Is there a name for such a function or a notation that is able to indicate such a characteristic?

CRoemheld
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1 Answers1

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Hint: You might want to have a look at Ackermann functions.

Markus Scheuer
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  • @epi163sqrt When I was looking through the Ackermann functions, I also encountered this particular section where it was denoted as $f|{x_i = g}$, do you think this would be applicable in my case? Something along the lines of $f{e_{x+1}}|{{x_2} = f{e_x}}$? Although I would have to rename the $x$ as $x_2$ is the argument, and not related to the $x$ in $e_x$. – CRoemheld Nov 01 '22 at 23:56