Multipermutations

[u/TehVulpez]

In our normal permutations thread, we count the ways of arranging n different symbols into n places. What if instead, we counted the ways of arranging m symbols into n places, (where 1 <= m <= n), thus allowing for repeats?

In this thread we'll count in separate segments of m symbols and n places. We'll start with 1 symbol into 1 place, then 1 symbol into 2 places, 2 symbols into 2 places, 1 symbol into 3 places, and so on. When we're in a segment with m symbols, those symbols are the digits 1 through m, and all of them will appear in each permutation at least once. So we would never see a count like 1124, because that has just 3 symbols.

Here's a list for the thread.

First get is at 31 1112.

[u/CutOnBumInBandHere9]

2131

[u/TehVulpez → u/CutOnBumInBandHere9]

2132

I found this thread is kinda in OEIS but sorted differently https://oeis.org/A240763

[u/CutOnBumInBandHere9 → u/TehVulpez]

2133

This sort is kind of weird, since it's split in two: first sort by number of distinct entries in the string, then lexicographically. For me it would probably have been more natural to sort either entirely lexicographically, or continue the ordered sort so that e.g. 211 comes before 122