What you call a list is formally known as sequence. There was a question which symbol is for sequence concatenation. Unfortunately there is no accepted answer. Symbols ⋅, ⌒ (commentator actually used u2322, "frown" symbol but it's resisting my attempt to copy it) and ∥ are mentioned in comments.
According the Wikipedia article ∥ is an operator for concatenation of numbers (doesn't specify which set of numbers, probably ℕ) but doesn't say much about sequences. The same symbol is in my opinion more commonly used for parallelism so it may confuse the reader.
I haven't seen ⌒symbol before but commentators agree about it.
This is confusing because the usual way of writing integrals in differential forms leaves something implicit: the tangent $k$-vector of the manifold of integration, and the notation itself tends to make people confuse $\mathrm dx$---the cotangent basis vector associated with the coordinate $x$---with $dx$---the symbol that tells us we're integrating with respect to $x$.
Suppose you have an integral in differential forms
$$\int_M f(x,y) \, \mathrm dx \wedge \mathrm dy$$
It really means this:
$$\int_M f(x,y) \, (\mathrm dx \wedge \mathrm dy)(T_{(M)}) \, dx \, dy$$
where $T_{(M)}$ is the tangent 2-vector for the manifold of integration $M$. For instance, a common choice of orientation would be that $T_{(M)} = e_x \wedge e_y$. And naturally, $(\mathrm dx \wedge \mathrm dy)(e_x \wedge e_y) = 1$. So the integral would reduce to $\int_M f(x,y) \, dx \, dy$.
This approach naturally generates the relevant surface/volume elements one might need. Suppose you have some surface two-form $\omega$ on a sphere that you want to integrate. You would set up the integral like so:
$$\int_S \omega(\theta, \phi; e_\theta \wedge e_\phi) \, d\theta \, d\phi$$
Note that $e_\theta \wedge e_\phi = r^2 \sin \theta \, \hat \theta \wedge \hat \phi$, and this would be appropriate to use if $\omega$ is written in terms of unit forms instead of $\mathrm d \theta$ and $\mathrm d \phi$.
You can write all of these above in index notation if you like. Just remember that one should always use the tangent $k$-vector associated with the coordinates of integration--$e_\theta \wedge e_\phi$ in that sphere example--though the orientation of that tangent $k$-vector is not necessarily determined by the ordering of the coordinates. This may introduce minus signs, if the problem specifies such.
Most of the time, though, people mean to say that a manifold is oriented the same way as the coordinates are ordered.
Best Answer
As Arturo points out in the comments, this question is only meaningful for a list (or sequence), and not a set, since sets have no intrinsic order. A list can be considered as a function $F: \mathbb{N} \rightarrow S$. The notation you are seeking is simply $F^{-1}$, the inverse of $F$. For example, $F(x) = x^2$ corresponds to the list $(0, 1, 4, 9, 16, 25, 36, ...)$, and since $F(6) = 36$, we have $F^{-1}(36) = 6$ mapping the element 36 back to position 6.