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# [Haskell](https://www.haskell.org) + [hgl](https://gitlab.com/wheatwizrad/haskell-golfing-library), 30 bytes

```haskell
ic"|"<<tv(:".")><fl<ce '.'><eq
````

[Attempt This Online!](https://ato.pxeger.com/run?1=m708I7E4OzUnZ8FNxczcgvyiEoXC0sSczLTM1BSFgKLUnNKUVC6oRMDS0pI0XYubCmm2mclKNUo2NiVlGlZKekqadjZpOTbJqQrqeup2NqmFUHUOuYmZeQq2Cin5XAoKBcEKKgppCsYKSiWpxSVKCBEjBaWc_Lz01CIlFFXJiSVKEHMWLIDQAA)

### Explanation

This performs a cartesian product to get all possible ways to replace characters with `.`. It then filters for those that have exactly $n$ `.`s, and concatenates them with `|`s.

## Alternative version

```
(ic"|"<ic"."<<mm tl)<<mp"?"><pST<eL<P1
```

This version is much longer, but in my opinion it has better potential to be shorter than the above version if hgl were improved.

### Explanation

This adds a dummy character `?` to the front of the list then gets all ways to partition that list, and filters the list down to those that have $n+1$ parts. Then it takes removes the first character of each partition, and concatenates them back together with `.` as the separator. Finally it concatenates all those together with `|` as the separator.

# Reflection

## Reflections on the 30 byte version
* `ce` and `eq` could be combined into a single function which checks if an element occurs exactly $n$ times.  This could actually be made to short circuit faster than `ce` and `eq` do by default.
* There should be a function that takes two elements and creates a list containing just those elements.  This could be done in terms of free monoids. It would not save bytes here since `(:".")` is so short, but it is close to being useful here.

## Reflections on the alternative version
* There should be a function to partition a list into chunks of a certain size.
* I could really use `m4` both as a prefix or an infix here.
* Here I do a two dimensional intercalation using two `ic`s.  There could be a builtin that does this.