What could be a (good) mathematical operation/function that would take a certain number of $n$-dim vectors and always outputs a unique $m$-dim vector, the uniqueness of which also depends up on the order in which the input vectors appear. Here, its recommended that $n$ is equal to $m$, but could be different as well.
Example operations:
Suppose I have vectors $a$, $b$, $c$ and $d$ with same dimensions such that,
- $f(f(f(a, b), c), d) = h$
- $f(f(f(a, c), d), b) = g$
- $f(f(f(a, d), b), c) = j$
- All outputs which are unique (in terms of magnitude and direction), in our case $g$, $h$ and $j$ should have the same dimension regardless of number of inputs