Hi. I hope this is the right forum.

Here's what I did:

I took all the permutations of 1234 and arranged them based on how much the digits of any group of permutations are spread out. In every group, the next permutation is obtained by increasing every digit of the previous one by 1 (4 loops back to 1).

I got 6 groups of 4 permutations.

The first one: 1234, 2341, 3412, 4123 - I call this group type 000 because, for example, in 1234 you skip 0 numbers between 1 and 2, between 2 and 3, between 3 and 4, and between 4 and 1 (4 loops back to 1).

The second group: 1243, 2314, 3421, 4132 - type 012 because, for example, in 4132 you skip 0 digits between 4 and 1, skip 1 digit (the 2) between 1 and 3, and skip 2 digits (4 and 1) between 3 and 2.

I hope you get the idea.

The remaining groups are:

The third group: 1342, 2413, 3124, 4231 - type 101

The fourth group: 1423, 2134, 3241, 4312 - type 210

The fifth group: 1324, 2431, 3142, 4213 - type 121

The sixth group: 1432, 2143, 3214, 4321 - type 222

What is this idea called? Is there a concept in mathematics that captures it? I spent a few hours browsing various articles on Wikipedia and didn't find this exact grouping of permutations.