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We need additional resources to handle "general" sequences of infinite exponentials. In particular: $\mathbf{Definition:}$ Suppose $A_k=\{a_1,a_2,\ldots,a_k\}$, $k\in\mathbb{N}$, with $a_k>0$ and $n\le |A_k|=k$. A general infinite exponential is: $$e_n(A_k) = \begin{cases} a_k, & \text{if $n=1$} \\ a_{k-n+1}^{e_{n-1}(A_k)}, & \text{if $n>1$} ...


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When I studied the various known matrices of combinatorical numbers I also looked at the following idea: what if we discuss functions with a set of results, not only one number? So for instance the concept of sine and cosine gets some special charme if we look not only at f(x) = sin(x), g(x)=cos(x) but at 2x2-matrices containing cos() and sin() and the input ...



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