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I've had this particular structure crop up multiple times in various topics related to applied statistics - rotating the points around the path leaves certain quantities of interest unchanged (e.g row and column sums, a very useful property in some contexts).

Presumably this is a very standard kind of object but I don't know the right kind of terms to look for information and results. I have a couple of simple conjectures I'd like to check for rather than try to prove from scratch, and even more would like to find results that might be useful that I haven't even considered yet.

Any suggestions appreciated, even something simple like a wikipedia page would be a good start

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