For the signature of $(\sigma, n)$, where $\sigma:N\rightarrow N$ and $n\in N$.
I think you could have something like:
$$ N\times N\times N $$
but I want it to be explicit that the there's a numeric function at index 1 and a number at index 2. I also need this to express that the function is partial.
Do either of these work:
$$ (N\times N)\times N $$ $$ N\rightarrow N \times N $$
Is $A\rightarrow B$ the set of all bijections from elements of $A$ to $B$? I'm assuming it isn't as the notation $f: A\rightarrow B$ would be redundant ($f\in A\rightarrow B$)